MA 15400 Course Assignments
Fall 2019

 

Class meeting Topic Assignment


Monday,
August 26

 

 Section 7.1
Periodic Functions		 Welcome to our class. Check out the schedule for Welcome Week.

Handouts: Ferris Wheel  (See pictures of the London Eye: 1  2 3)
                Syllabus
                Practice Questions to Check Prerequisite Skills Needed for MA 15400

Today's objectives:
 1. Identify if a graph represents a periodic function.
 2. Determine period, amplitude and midline.
 3. Use a graph to find and interpret y if given t or vice versa.

Due: Wednesday, August 28
Read: General Course Information, the Syllabus, and, if you have the text, Section 7.1 and 7.2
Do:    If necessary, purchase a TI-84 Plus CE or equivalent and purchase eHW access.
           Note: access is good for one year.
           Practice on eHW Flash Cards: 7.1 Periodic Functions.
           Optional: Section 7.1 -- your choice of 1-17, 23-34 as needed.
           Review eHW Math Background Needed for MA 15400 and eHW Flash Cards for Prerequisite Skills 
           See also Practice Questions to Check Prerequisite Skills Needed for MA 15400 and these Worked out Solutions.
           You should also be proficient in these skills needed for MA 15300.

Prepare for QUIZ 1 next Wednesday, Sept 4 over prerequisite skills. (See green packet and eHW.)

Due Friday, August 30, 11:59 pm: E-HW: Quiz on John's Syllabus- Score 90% or Higher by the Deadline!
Note: You need to get a score of 90% or higher for this eHW by the deadline to open up any future eHW assignments.
You have unlimited attempts.

Due Tuesday, Sept 3, 11:59 pm:  E-HW: Math Background Needed for MA 15400
Due Tuesday, Sept 3, 11:59 pm:  E-HW0: General Course Information and Using eHW

Wednesday,
August 28		 Section 7.2
The Sine Function
(and its Sidekick, Cosine)
Today's objectives:
  1. Sketch the position of a point on a circle of radius r corresponding to a given angle (or value of time or number of revolutions) and give its coordinates
  2. Find angles between 0° and 360° which have the same sine or cosine of a given angle.
    Determine in which quadrant an angle lies if given certain conditions.


Do (for practice): 
Flash Card 7.2 Report the coordinates of a point on a circle of radius r given the angle.
Flash Card 7.2 Use the definitions of sine and cosine
If you have a text, see read Section 7.3 and do Section 7.2 -- 1, 3, 5-31
Click on the photo to enlarge (and download for printing).

Prepare for QUIZ 1 next Wednesday, Sept 4 over prerequisite skills.
(See the green packet with KEY and eHW Flash Cards for practice.)

Due Friday, August 30, 11:59 pm: E-HW: Quiz on John's Syllabus- Score 90% or Higher by the Deadline!
Note: You need to get a score of 90% or higher for this eHW by the deadline to open up any future eHW assignments.
You have unlimited attempts.

Due Tuesday, Sept 3, 11:59 pm:  E-HW: Math Background Needed for MA 15400
Due Tuesday, Sept 3, 11:59 pm:  E-HW0: General Course Information and Using eHW  
Friday
August 30		 Section 7.3
Radians
Today's objectives:
  1. Convert an angle from degrees to radians and vice versa.
  2. Interpret the radian measure of the central angle of a circle of radius r as the number of radius lengths, r, that you need to wrap around the rim of the circle on the arc spanned by the angle.
  3. Understand the relationship between arc length, radius and an angle measure in radians.
    If given two of the arc length s, radius r, or an angle θ, find the third.
The radian measure of an angle θ is the number of radius lengths that a bug would walk on the rim of a circle spanned by the angle.
For a circle of radius r, if s is the arc length the bug walks on the rim, then we have
s = (the radius r) x (# of radius lengths) or
s =  r x θ

Here is a short video of the bug taking a tour around the rim of a circle,
counting radius lengths as he goes. It is a silent movie since bugs can't talk.

Suppose a central angle θ  in a circle of radius r spans an arc of length s. Measure how many radius lengths that the length of the arc is.  This number of radius lengths is the radian measure of the angle θ: we have rθ = s.

Do (for practice): 
Flash Card 7.3 Find points on a circle using radian measure of quadrantals
Flash Card 7.3 Radian Measure as Number of Radius Lengths Around a Circle
If you have a text, read Chapter 7 Skills Refresher, see Section 7.3 -- 1-56 as desired (for practice).

Prepare for QUIZ 1 next Wednesday, Sept 4 over prerequisite skills.
(See the green packet with KEY and eHW Flash Cards for practice.)

Due Tuesday, Sept 3, 11:59 pm:  E-HW: Math Background Needed for MA 15400
Due Tuesday, Sept 3, 11:59 pm:  E-HW0: General Course Information and Using eHW  
Due Friday, Sept. 6, 11:59 pm: E-HW 01 Sections 7.1 - 7.2
Due Wednesday, Sept. 11, 11:59 pm: E-HW 01 Sections 7.3
Class meeting Topic Assignment
Mon, Sept. 2 Labor day holiday No class meeting
Wed., Sept. 4 Chapter 7 Skills Refresher
Special Angles		 Today:  QUIZ 1 over Prerequisites. We briefly looked at special angles

Do (for practice): 
Flash Card Ch 7 Skills Refresher Properties of Special Triangles
Flash Card Ch 7 Skills Refresher Exact Values of Sine and Cosine
 If you have a text, see Chapter 7 Skills Refresher (page 325) -- 25-30

Due Friday, Sept. 6, 11:59 pm: E-HW 01 Sections 7.1 - 7.2
Due Wednesday, Sept. 11, 11:59 pm: E-HW 02 Sections 7.3
Due Friday, Sept. 13: Writing Assignment 1: Bug on a Square Track
For next class, Fri., Sept. 6, please come prepared with the first two pages of WR1 completed.

Fri., Sept. 6 Chapter 7 Skills Refresher
Special Angles cont'd		 Today's objectives:
1. Find exact values of sine and cosine for multiples of 30°, 45°, and 60° or their radian equivalents π/6, π /4, or π /3.
2. Use proportional reasoning to find sides of special triangles.

Do (for practice):
Flash Card Ch 7 Skills Refresher Properties of Special Triangles
Flash Card Ch 7 Skills Refresher Exact Values of Sine and Cosine
If you have a text, see Chapter 7 Skills Refresher  (page 324) -- 1 - 24, 26-31 

Due tonight, Friday, Sept. 6, 11:59 pm: E-HW 01 Sections 7.1 - 7.2
Due Wednesday, Sept. 11, 11:59 pm: E-HW 02 Sections 7.3
Due Friday, Sept. 13, 11:59 pm: E-HW 03 Chapter 7 Skills Refresher
Due Friday, Sept. 13: Writing Assignment 1: Bug on a Square Track

Prepare for QUIZ 2 next Monday, Sept. 9 over 7.1 and 7.2
Class meetingg Topic Assignment
Mon, Sept. 9 Section 7.4
Graphs of the Sine and Cosine (and Outside Changes to the Formula)		 Today:  QUIZ 2 over 7.1 and 7.2
We explored the graph of y = Asin(x) + k (Outside additive and multiplicative changes)

Today's objectives:
1. Solve simple trig equations over a requested interval; for example on the interval [0, 2π) find θ if sin θ = 1/2, providing exact values of angles measured in radians when they are multiples of π/6, π /4, or π /3. Be aware of when more than one solution exists! Be able to sketch the angle or angles.
2. Know the main characteristics (period, amplitude, midline, domain, range, odd/even symmetry, when it is positive, negative, increasing, decreasing, if it starts at or above the midline) of the graph of y = sin θ, and y = cos θ. Relate this to the unit circle as the x-coordinate (cosine) or the y-coordinate (sine) of the point on the circle.
3. For y = Asin(x) + k or y = Acos(x) + k , identify the period, amplitude, and midline.

We discussed the domain, range, period, and amplitude of y = sin(x) and y = cos(x) and how these can be determined from the unit circle.
We looked at an outside change to the function, which results in the original function being transformed vertically (change to the output).

  1. y = Asin(x) and y = Acos(x) have amplitude |A|. 
    For A > 0, 
    the graph of y = Asin(x) vertically stretches or compresses the graph of  y = sin(x) by A units.
    the graph of y = –Asin(x) is a vertical reflection of the graph of y = Asin(x).
    Similarly for y = cos(x).  
     

  2. y = sin(x) + k and y = cos(x) + k have midline k.
    For k > 0, 
    the graph of y = sin(x) + k vertically shifts the graph of y = sin(x) up k units.
    the graph of y = sin(x) – k vertically shifts the graph of y = sin(x) down k units.
    Similarly for y = cos(x).  

The first multiplies the output by a quantity; the second adds/subtracts a quantity to the output.

Do (for practice):
Flash Card 7.4 Period, Amplitude, Midline
If you have a text, see Section 7.4 -- 1-24, 26-30, 34-38

Due Wednesday, Sept. 11, 11:59 pm: E-HW 02 Sections 7.3
Due Friday, Sept. 13, 11:59 pm: E-HW 03 Chapter 7 Skills Refresher
Due Friday, Sept. 13: Writing Assignment 1: Bug on a Square Track
Due Monday, Sept. 16: Writing Assignment 2: What's My Angle?
Wed., Sept. 11  

Section 7.5
The graph of
y = sin(Bx)
(Inside multiplicative change)

 For the function y = AsinBx + k
we explored the effects of  B on the period to find that,
for positive values of B, this graph has a period of 2π/B, an amplitude of  |A|, and midline which is y = k.
 

Today's objectives:
1. Report the period of the graph of y = AsinBx + k.
2. If you have found the period, p, of  y = sinBx, check that your value is correct by substituting into the formula and verifying that B·p = 2π.
3. Given a graph, report the midline, amplitude and period and use them to find the formula y = AsinBx + k or y = AcosBx + k.


Do (for practice)::
Flash Card 7.4 Period, Amplitude, Midline
 Flash Card 7.5 Find a Formula of a Sine or Cosine Function (No Phase Shift Needed)
Flash Card 7.5 Find a Formula of a Sine or Cosine Function (Ferris Wheel) - then find y if given x
 Flash Card 7.5 Find a Formula of a Sine or Cosine Function (Ferris Wheel) - then find x if given y
 If you have a text, see Section 7.5 -- 1-12, 21-26

Due tonight, Wednesday, Sept. 11, 11:59 pm: E-HW 02 Sections 7.3
Friday, Sept. 13: QUIZ 3 over 7.3 and Chapter 7 Skills Refresher

Due Friday, Sept. 13, 11:59 pm: E-HW 03 Chapter 7 Skills Refresher
Due Friday, Sept. 13: Writing Assignment 1: Bug on a Square Track
Due Monday, Sept. 16: Writing Assignment 2: What's My Angle?
Fri., Sept. 13 Section 7.5
The graph of
y = Asin(B(x−h))
(Inside additive change)

 

 Today:  Continued Section 7.5. If given a graph, find the midline, period, amplitude, and the horizontal and phase shifts. When specifying horizontal and phase shift, include whether it is regular sine or cosine (or upside down versions of these), whether it is shifted left or right, and by how much.

 Today's objectives:
1. Given a graph and a model choice (regular or upside down sine or cosine) report the phase shift.
2. Given a graph with a nonzero phase shift φ or horizontal shift h, find a formula y = Asin(B(x−h))+ k or y = Asin(Bx−φ) + k.
3. If you have found the phase shift, φ, of the graph of y =sin(Bx−φ), check that your value is correct by multiplying out y =sin(B(x−h))
and verifying that B·h = φ, where h is the horizontal shift.
 

Do (for practice)::
Flash Card 7.5 Find Phase Shift
 Flash Card 7.5 Find a Formula of a Sine or Cosine Function (Phase Shift Needed)
If you have a text, see Section 7.5 -- 27-31, 37, 38, 44-50

Due tonight, Friday, Sept. 13, 11:59 pm: E-HW 03 Chapter 7 Skills Refresher
Due Monday, Sept. 16: Writing Assignment 2: What's My Angle?
Due Friday, Sept. 20, 11:59 pm: E-HW 04 Section 7.4-7.5
Class meetingg Topic Assignment
Mon, Sept. 16
The Phase Shift (Cont'd) and Section 7.6
The Tangent Function		 Today's objectives:
1. If you have found the phase shift, φ, of the graph of y =sin(Bx−φ), check that your value is correct by multiplying out y =sin(B(x−h))
and verifying that B·h = φ, where h is the horizontal shift.
2. Know the main characteristics (period, domain, range, symmetry, value at π/4, when it is positive, negative, zero, undefined. increasing)
of the graph of y = tan θ.
3. Relate the graph of y = tan θ to the unit circle as the slope y/x of the line through the origin and the point on the circle.

Do (for practice):
Flash Card 7.5 Find Phase Shift
 Flash Card 7.5 Find a Formula of a Sine or Cosine Function (Phase Shift Needed)
Flash Card 7.6 Graph of y = AtanBx
If you have a text, see Section 7.6  -- 1-36
 
Due Friday, Sept. 20, 11:59 pm: E-HW 04 Section 7.4-7.5
Due Monday, Sept. 23: Writing Assignment 3: Trig Graphs
Wed., Sept. 18 Section 7.6 The Tangent Function (Cont'd) and  Section 7.7
Reciprocal Functions

Today's objectives:
1. Given the graph of y = AtanBx and its intercepts and vertical asymptotes, find A and B.
2. Given the formula of y = AtanBx, report its intercepts and vertical asymptotes (exact). Solve Atan Bx = A.
3. Find exact values of sin θ, cos θ, tan θ, csc θ, sec θ, cot θ if given the angle θ as a multiple of 30°, 45°, and 60° (or π/6, π/4, or π/3).
4. Find exact values of sin θ, cos θ, tan θ, csc θ, sec θ, cot θ if given the value of one of these trig functions.

 Do (for practice):
Flash Card 7.5 Find Phase Shift
 Flash Card 7.5 Find a Formula of a Sine or Cosine Function (Phase Shift Needed)
Flash Card 7.6 Graph of y = AtanBx
If you have a text, see Ch 7 Review 11, 12, 15, 19, 25, 27, 29 and 31 and Section 7.7  -- 1-25, 32-35

Friday, Sept 20: QUIZ 4 over 7.4 and 7.5

Due Friday, Sept. 20, 11:59 pm: E-HW 04 Section 7.4-7.5
Due Monday, Sept. 23: Writing Assignment 3: Trig Graphs
Test 1 next week in the Math Test Center. See BB for a review sheet and details in the folder Review for Exams.
Fri., Sept. 20 Section 7.7
Reciprocal Functions		 Today's objectives:
1. Find exact values of sin θ, cos θ, tan θ, csc θ, sec θ, cot θ if given the angle θ as a multiple of 30°, 45°, and 60° (or π/6, π/4, or π/3).
2. Find exact values of sin θ, cos θ, tan θ, csc θ, sec θ, cot θ if given the value of one of these trig functions.

 Do (for practice):
Flash Card 7.7 Find exact values of all six trig functions of any angle
If you have a text, see Section 7.7  -- 1-35, 37, 38, 44-50

Due tonight, Friday, Sept. 20, 11:59 pm: E-HW 03 Section 7.4 and 7.5
Due Monday, Sept. 23: Writing Assignment 3 Trig Graphs

Test 1 next week. See Review Sheet. This is in the folder Reviews for Exams on Blackboard.

Class meetingg Topic Assignment
Mon, Sept. 23
Section 7.8 Inverse Trig Functions		 Today's objectives:
1. Solve simple trig equations over a requested interval; for example [0, 2π), [0,360°), (−∞,∞), or other intervals, providing
   a. exact values of angles measured in radians (when given special angles as in 1a above)
   b.decimal approximations using the inverse trig functions
2. Distinguish the meaning of the notation sin−1x, arcsin x, sin2x, sin x2, csc x, etc.
3. Interpret tan θ as the slope of the angle of inclination.

Do (for practice):
Flash Card 7.8 Solve trig equations for the exact value of the angle WITHOUT a calculator
Flash Card 7.8 Solve trig equations for the approximate value of the angle WITH a calculator
Flash Card 7.8 Given the slope, find the angle of inclination
If you have a text, see Section 7.8 - - 1-33
 
 Due Wednesday, Oct. 2, 11:59 pm: E-HW 05 Section 7.7 and 7.8
 
Wed., Sept. 25 Today: Section 8.1 Right Triangle Trigonometry:  SohCahToa and Pythagoras

 

Today's objectives:
1. If given any two of the side lengths of a right triangle, find the remaining parts. 
2. If given a side length and an angle of a right triangle, find the remaining parts. 

Due Monday, Sept. 30
Flash Card 8.1 Given the slope, find the angle of inclination
Flash Card 8.1 Use right triangle definitions if given two sides
Flash Card 8.1 Use right triangle definitions if given the angle and a side
Flash Card 8.1 Use right triangle definitions - applications
If you have a text, see Section 7.8 - - 1-33
Do: Section 8.1  -- 1-47 as desired.
Due Wednesday, Oct. 2, 11:59 pm: E-HW 05 Section 7.7 and 7.8
 Due Friday, Oct. 4, 11:59 pm: E-HW 06 Section 8.1
 Due Monday, Oct. 7: Writing Assignment 4: The Gateway Arch

The test is outside of class in the Math Test Center (KT G18).
Covers: Chapters 7.1 - 7.5, Chapter 7 Skills Refresher, your Writing Assignments WR1, WR2, and WR3 and your past quizzes and eHW assignments.
Walk in with any kind of photo ID and your graphing calculator to take the test.
Math Test Center (KT G18) is open:
  Wed., Sept. 25,  after class - 7:00 PM (it closes at 8:00 pm)
  Thurs., Sept. 26, 9:00 AM - 7:00 PM (it closes at 8:00 pm)
  Friday, Sept. 27, 9:00 AM - 3:30 PM (it closes at 4:30 PM)

See the Review Sheet. This is in the folder Reviews for Exams on Blackboard.
Fri., Sept. 27 No class meeting Test 1 is available in the Test Center, KT G18, if you have not yet taken it.
Due Wednesday, Sept. 24
 Read: Section 8.1 and 8.2
Do: Section 8.2  -- 1-5, 7, 8, 32 - 35, 37, 41

Due Wednesday, Sept. 26, 11:59 pm: E-HW 05 Section 7.7 and 7.8
 Due Friday, Sept. 28, 11:59 pm: E-HW 06 Section 8.1 Right Triangle Trigonometry
 Due Monday, Oct. 7: Writing Assignment 4: The Gateway Arch
Class meetingg Topic Assignment
Mon, Sept. 30
Section 8.2
Law of Sines		 Today's objectives:
1. Solve for sides and angles of a triangle using the Law of Sines.
2. Determine when you can use SohCahToa and Pythagoras and when you can use the Law of Sines. 

Do (for practice):
Flash Card 8.2 Use Law of Sines to Solve Triangles
 If you have a text, see Section 8.2 - - 1-5, 7, 8, 32 - 35, 37, 41
 
 Due Wednesday, Oct. 2, 11:59 pm: E-HW 05 Section 7.7 and 7.8
 Due Friday, Oct. 4, 11:59 pm: E-HW 06 Section 8.1
 Due Monday, Oct. 7: Writing Assignment 4: The Gateway Arch
Wed., Oct. 2 Section 8.2
Law of Cosines		 Today's objectives:
1. Solve for sides and angles of a triangle using the Law of Cosines.
2. Determine when you can use the Law of Cosines and when you can use the Law of Sines. 

Do (for practice):
Flash Card 8.2 Use Law of Cosines to Solve Triangles
 Flash Card 8.2 Use Law of Sines and Cosines to Solve Triangles
 If you have a text, see Section 8.2 - - 6, 36,40, 42-44, 47
 
 Due tonight, Wednesday, Oct. 2, 11:59 pm: E-HW 05 Section 7.7 and 7.8
 Due Friday, Oct. 4, 11:59 pm: E-HW 06 Section 8.1
 Due Monday, Oct. 7: Writing Assignment 4: The Gateway Arch
 Due Friday, Oct. 11, 11:59 pm: E-HW 07 Section 8.2
Friday, Oct. 4: QUIZ 5 over Section 7.6. 7.7. 7.8
Class meetingg Topic Assignment
Mon, Oct. 7
Polar Coordinates (8.3) and Solving Trig Equations Graphically (9.1)		 Today's objectives:
1. Convert coordinates from polar to rectangular and vice versa
2. Solve a trig equation graphically.

Do (for practice):
Flash Card 8.3 Convert Polar => Rectangular (WITH or WITHOUT a calculator)
 Flash Card 8.3 Convert Rectangular=> Polar (WITH or WITHOUT a calculator)
 Flash Card 9.1 Solving Trig Equations Graphically
 If you have a text, see Section 8.3  --1-22 and Section 9.1  -- 1-11, 15-31, 33, 34, 38, 39, 41
Due Friday, Oct. 11, 11:59 pm E-HW 07 Section 8.2 Law of Sines and Cosines
Due Monday, Oct. 14: Writing Assignment 5: Law of Sines and Cosines to the Rescue
Due Monday, Oct. 14, 11:59 pm E-HW 08 Section 8.3 and 9.1
Wed., Oct. 9 Trig Identities (9.2) Today's objectives:
1. Rewrite trigonometric expressions.
2. Build fractional fluency.

Do (for practice):
Flash Card 9.2 Trigonometric Identities
Flash Card 9.2 Use Identities to Rewrite Trig Expressions into Algebraic Expressions
 If you have a text, see Section 9.2  -- 1-12, 14, 16-26, 31, 32 and Worksheet (see BB).  For more see Section 7.7 -- 8-15

Due Friday, Oct. 11, 11:59 pm E-HW 07 Section 8.2 Law of Sines and Cosines
Due Monday, Oct. 14: Writing Assignment 5: Law of Sines and Cosines to the Rescue
Due Monday, Oct. 14, 11:59 pm E-HW 08 Section 8.3 and 9.1
Due Wednesday, Oct. 16, 11:59 pm: E-HW 09 Section 9.2 Identities

Friday, Oct. 11: QUIZ 6 over Section 8.1 and 8.2
Fri., Oct. 11 Using Identities to Rewrite Trig Expressions into Algebraic Expressions (9.2) Today's objectives:
1. Use the double angle trig identities.
2. Write trigonometric expressions into algebraic expressions.

Do (for practice):  
 Flash Card 9.2 Trigonometric Identities
Flash Card 9.2 Use Identities to Rewrite Trig Expressions into Algebraic Expressions
 If you have a text, see Section 9.2  -- 13, 15, 27 - 30, 35, 54 - 58

Due Friday, Oct. 11, 11:59 pm E-HW 07 Section 8.2 Law of Sines and Cosines
Due Monday, Oct. 14: Writing Assignment 5: Law of Sines and Cosines to the Rescue
Due Monday, Oct. 14, 11:59 pm E-HW 08 Section 8.3 and 9.1
Due Wednesday, Oct. 16, 11:59 pm: E-HW 09 Section 9.2 Identities
Class meeting Topic Assignment
Mon, Oct. 7 Trig Equations (9.2) and Sum and Difference Identities (9.3) Today's objectives:
1. Use the trig identities to solve trig equations algebraically with graphical support.
2. Use sum and difference identities.

Do (for practice):  
 Flash Card 9.2 Trigonometric Identities
Flash Card 9.2 Use Identities to Rewrite Trig Expressions into Algebraic Expressions
Flash Card 9.2 Solving Trigonometric Equations by factoring
Flash Card 9.3 Using Sum and Difference Identities
If you have a text, see Section 9.2  -- 13, 15, 27 - 30, 35, 54 - 58

Due tonight, Monday, Oct. 14, 11:59 pm E-HW 08 Section 8.3 and 9.1
Due Wednesday, Oct. 16, 11:59 pm: E-HW 09 Section 9.2 Identities
Due Wednesday, Oct. 23, 11:59 pm: E-HW 10 Section 9.2 and 9.3
Due Friday, Oct. 25: Writing Assignment 6: Using Trig Identities
Wed. Oct. 16 Function Composition, Decomposition (10.1) and Inverses (10.2) Today's objectives:
1. Use function composition and decomposition
2. Find the inverse of a one-to-one function

Do (for practice):  
Flash Card 10.1 Composition of Functions
Flash Card 10.1 Decomposition of Functions: Given f(g(x)) and g, find f
Flash Card 10.1 Decomposition of Functions: Given f(g(x)) and f, find g
Flash Card 10.2 Given the Formula of an Invertible Function, Find Its Inverse (Level 1)
 If you have a text, see Section 10.1 -- 4-25, 31, 37-50, 64, 65 and Section 10.2 -- 1-10, 12-34, 37-43, 47-49, 58, 82

Due tonight, Wednesday, Oct. 16, 11:59 pm: E-HW 09 Section 9.2 Identities
Due Wednesday, Oct. 23, 11:59 pm: E-HW 10 Section 9.2 and 9.3
Due Friday, Oct. 25: Writing Assignment 6: Using Trig Identities

 Friday, Oct. 18: QUIZ 7 on 8.3 and 9.1
Fri., Oct. 18 Vectors (12.1)

Today's objectives:
1. Given the sketch of a vector, use a grid to sketch the result of scalar multiplication or the opposite of the vector.
2. Given the sketch of vectors, use a grid and the "head to tail" method to sketch the result of vector addition or subtraction.

Do (for practice):
Flash Card 12.1 Vectors - Adding Geometrically with a Grid
Flash Card 12.1 Use a Grid to Perform Vector Arithmetic
 If you have a text, see Section 12.1 -- 1-15 and Chapter 12 Review -- 34, 35, 37
 
Due Wednesday, Oct. 23, 11:59 pm: E-HW 10 Section 9.2 and 9.3
Due Friday, Oct. 25, 11:59 pm: E-HW 11 Section 10.1-10.2 Composition, Decomposition, and Inverses
Due Friday, Oct. 25: Writing Assignment 6: Using Trig Identities

No class meeting Monday, Oct. 21. Enjoy Fall Break!
Class meeting Topic Assignment
Mon., Oct. 21 No class meeting  
Rhino on Fall Break Fall Break

Take a Rhino Rest!
 
Wed., Oct. 23 Component Form of Vectors (12.2)

Today's objectives:
1. Resolve a vector into horizontal and vertical components given its magnitude and direction.
2. Given the horizontal and vertical components of a vector, report its magnitude and direction.
3. Perform vector arithmetic.

Do (for practice):
Flash Card 12.1 Vectors - Adding Geometrically with a Grid
Flash Card 12.1 Use a Grid to Perform Vector Arithmetic
Flash Card 12.2 Vectors - Writing in Component Form
Flash Card 12.2 Vectors - Finding the Magnitude
Flash Card 12.2 Vector Addition Involving Horizontal or Vertical Vectors
Flash Card 12.2 Two-dimensional Vector Arithmetic

 If you have a text, see Section 12.1 -- 16-20, 24 and 12.2 -- 1-2, 4, 5, 8, 13-18, 21, 23, 25-27 and Chapter 12 Review -- 12, 29, 34, 35, 37
 
Due tonight, Wednesday, Oct. 23, 11:59 pm: E-HW 10 Section 9.2 and 9.3
Due Friday, Oct. 25, 11:59 pm: E-HW 11 Section 10.1-10.2 Composition, Decomposition, and Inverses
Due Friday, Oct. 25: Writing Assignment 6: Using Trig Identities
Due Monday, Nov. 4, 11:59 pm: E-HW 12 Section 12.1-12.2 Component Form of Vectors

Friday, Oct. 25: QUIZ 8 on 9.2 and 9.3

Test 2 is outside of class in the Math Test Center (KT G18) next week.
See the Review Sheet in the folder Reviews for Exams on Blackboard.
Fri., Oct. 25 Combining Forces (12.3) Today's objectives:
1. Resolve a vector into horizontal and vertical components given its magnitude and direction.
2. Given the horizontal and vertical components of a vector, report its magnitude and direction.
3. Perform vector arithmetic.

Do (for practice):
Flash Card 12.3 Combining Forces

If you have a text, see Section 12.3 -- 1-14, 16,17, 19 and Chapter 12 Review -- 12, 29, 34, 35, 37
 
Due tonight, Friday, Oct. 25, 11:59 pm: E-HW 11 Section 10.1-10.2 Composition, Decomposition, and Inverses
Due Monday, Nov. 4, 11:59 pm: E-HW 12 Section 12.1-12.2 Component Form of Vectors
Due Wednesday, Nov. 6, 11:59 pm: E-HW 13 Section 12.3 Application of Vectors
 
Test 2 is available outside of class beginning Tuesday, Oct. 29 up until Thursday, Oct. 31.
See Review Sheet. This is in the folder Reviews for Exams on Blackboard.
Class meeting Topic Assignment
Mon., Oct. 28 n-dimensional Vectors (12.3) and Sequences (13.1) Today's objectives:
1. Perform vector arithmetic for a vector of n-dimensions, n ≥ 2.
2. Classify a sequence as arithmetic, geometric, or neither and find a formula for its nth term.

 Do (for practice):
Flash Card 12.3 n-Dimensional Vector Arithmetic
Flash Card 13.1 Classifying Sequences: Is it Arithmetic?
Flash Card 13.1 Classifying Sequences: Is it Geometric?
Flash Card 13.1 Given graph, find the nth term of a sequence
Flash Card 13.1 Given terms, find the nth term of a sequence
Flash Card 13.1 Applications of Sequences

 If you have a text, see Section 12.3 -- 1-13 and Section 13.1 -- 1-48

Due Monday, Nov. 4, 11:59 pm: E-HW 12 Section 12.1-12.2 Component Form of Vectors
Due Wednesday, Nov. 6, 11:59 pm: E-HW 13 Section 12.3 Application of Vectors
Due Friday, Nov. 8, 11:59 pm: E-HW 14 Section 13.1 Sequences

Test 2 is available outside of class beginning Tuesday, Oct. 29 up until Thursday, Oct. 31.
See Review Sheet. This is in the folder Reviews for Exams on Blackboard.
 No class meeting Wed. Oct. 30. 
Wed., Oct. 30 No class meeting Take Test 2 in Math Test Center
Fri., Nov. 1 Series and
Adding like Gauss (13.2)		 Today's objectives:
1. Find a formula for the nth term of an arithmetic or geometric sequence.
2. Find the sum of an arithmetic series using an efficient strategy (like what Gauss did).

Do (for practice):
Flash Card 13.2 Adding like Gauss - given the number of terms
If you have a text, see Section 13.2 -- 1-4, 21, 26-30, 42, 45

Due Monday, Nov. 4, 11:59 pm: E-HW 12 Section 12.1-12.2 Component Form of Vectors
Due Wednesday, Nov. 6, 11:59 pm: E-HW 13 Section 12.3 Application of Vectors
Due Friday, Nov. 8, 11:59 pm: E-HW 14 Section 13.1 Sequences
Due Wednesday, Nov. 13: Writing Assignment 7: Wilbur's Trough
Monday, Nov. 4: QUIZ 9 on 10.1-10.2, 12.1-12.3
Class meeting Topic Assignment
Mon., Nov. 4 Sigma Notation (13.2) Today's objectives:
1. Find the sum of an arithmetic series using an efficient strategy (like what Gauss did).
2. If given a series in expanded notation, write it in sigma notation or vice versa.

Do (for practice):
Flash Card 13.2 Adding like Gauss - given the number of terms
Flash Card 13.2 Adding like Gauss
Flash Card 13.2 Given sigma notation, write in expanded form
Flash Card 13.2 Given expanded form, write in sigma notation

If you have a text, see Section 13.2 -- 1-4, 21, 26-30, 42, 45

Due tonight, Monday, Nov. 4, 11:59 pm: E-HW 12 Section 12.1-12.2 Component Form of Vectors
Due Wednesday, Nov. 6, 11:59 pm: E-HW 13 Section 12.3 Application of Vectors
Due Friday, Nov. 8, 11:59 pm: E-HW 14 Section 13.1 Sequences
Due Monday, Nov. 11, 11:59 pm: E-HW 15 Section 13.2 Series
Due Wednesday, Nov. 13: Writing Assignment 7: Wilbur's Trough
Wed., Nov. 6 Finite Geometric Series (13.3) Today's objectives:
1. If given a series in expanded notation, write it in sigma notation or vice versa.
2. Determine the sum of a finite geometric series using the formula.

Do (for practice):
 Flash Card 13.2 Given sigma notation, write in expanded form
Flash Card 13.2 Given expanded form, write in sigma notation
Flash Card 13.3 Finite Geometric Series

If you have a text, see Section 13.2 -- 5-15, 11-25, 34-37, 42, 43, 45 and Section 13.3 -- 1-17, 20-26

Due tonight, Wednesday,  Nov. 6, 11:59 pm: E-HW 13 Section 12.3 Application of Vectors
Due Friday, Nov. 8, 11:59 pm: E-HW 14 Section 13.1 Sequences
Due Monday, Nov. 11, 11:59 pm: E-HW 15 Section 13.2 Series
Due Wednesday, Nov. 13: Writing Assignment 7: Wilbur's Trough
Fri., Nov. 8 Infinite Geometric Series (13.4) Today's objectives:
1. Determine the sum of a finite geometric series using the formula.
2. Determine the sum of an infinite geometric series.

Do (for practice):
 Flash Card 13.4 Infinite Geometric Series - find the sum
Flash Card 13.4 Applications of Infinite Geometric Series

If you have a text, see Section 13.4 -- 1-17, 24-26  and Chapter 13 Review -- 4-9

Due tonight, Friday, Nov. 8, 11:59 pm: E-HW 14 Section 13.1 Sequences
Due Monday, Nov. 11, 11:59 pm: E-HW 15 Section 13.2

Due Wednesday, Nov. 13: Writing Assignment 7: Wilbur's Trough

Due Friday, Nov. 15, 11:59 pm: E-HW 16 Section 13.3-3.4

Class meeting Topic Assignment
Mon., Nov. 11 Infinite Geometric Series (13.4) and Parametric Equations (14.1) Today's objectives:
 1. Determine the sum of an infinite geometric series.
 2. Given graphs of two parametric equations, sketch the path of the object.

For fun, see Proofs Without Words.

Do (for practice):
Flash Card 13.4 Infinite Geometric Series - find the sum
Flash Card 13.4 Applications of Infinite Geometric Series

If you have a text, see Section 13.4 -- 8-13 and Chapter 13 Review --24
(See BB for a link to this chapter.)
 
Due tonight, Monday, Nov. 11, 11:59 pm: E-HW 15 Section 13.2
Due Wednesday, Nov. 13: Writing Assignment 7: Wilbur's Trough
Due Friday, Nov. 15, 11:59 pm: E-HW 16 Section 13.3-3.4
Due Wednesday, Nov. 20, 11:59 pm: E-HW 17 Section 14.1

Quiz 10 Opportunity on 13.1-13.2 for Wednesday, Nov. 13.
Wed., Nov. 13 Parametric Equations (14.1)

Today's objectives:
1. Given graphs of two parametric equations x = f(t) and y = g(t), sketch the path of the object (y vs. x).
2. Given equations of two parametric equations x = f(t) and y = g(t), eliminate the parameter to write y in terms of x.

Do (for practice):
Flash Card 14.1 Parametric Equations - Use Graphs to Parametrize
Flash Card 14.1 Parametric Equations - Eliminate the Parameter

If you have a text, see Section 14.1 -- 1-43 (See BB for a link to this chapter.)
 
Due Friday, Nov. 15, 11:59 pm: E-HW 16 Section 13.3-3.4
Due Wednesday, Nov. 20, 11:59 pm: E-HW 17 Section 14.1
Fri., Nov. 15 Circles (14.2) Today's objectives:
1. Given equations of two parametric equations x = f(t) and y = g(t), eliminate the parameter to write an implicit equation involving y and x.
2. Given the implicitly defined formula of a circle, report its center and radius
3. Given the graph of a circle, report its center, radius, and formula in implicit and parametric form.

Do (for practice):
Flash Card 14.1 Parametric Equations - Eliminate the Parameter
Flash Card 14.2 Circles: Given implicitly defined formula, report center and radius
Flash Card 14.2 Circles: Given graph, report center, radius, and formula

If you have a text, see Section 14.2 -- 1-26, 28, 29 (See BB for a link to this chapter.)
 
Due tonight, Friday, Nov. 15, 11:59 pm: E-HW 16 Section 13.3-3.4
Due Wednesday, Nov. 20, 11:59 pm: E-HW 17 Section 14.1
Due Monday, Nov. 25, 11:59 pm: E-HW 18 Section 14.2 and 14.3

 Due Monday, Nov. 25: Writing Assignment 8: Job Offer
Class meeting Topic Assignment
Mon., Nov. 18 Circles (14.2) and Ellipses (14.3) Today's objectives:
1. Given equations of two parametric equations x = f(t) and y = g(t), eliminate the parameter to write an implicit equation involving y and x.
2. Given the implicitly defined formula of a circle or an ellipse, report its formula in parametric form and other important properties.
3. Given the graph of a circle or ellipse, report its formula in implicit and parametric form and other important properties.

Do (for practice):
Flash Card 14.2 Circles: Given implicitly defined formula, report center and radius
Flash Card 14.2 Circles: Given graph, report center, radius, and formula
Flash Card 14.3 Ellipses: Given implicitly defined formula, report center, vertices, etc.
Flash Card 14.3 Ellipses: Given graph, report center, vertices, and formula
If you have a text, see Section 14.3 -- 1-10, 11a, 18, 19 (See BB for a link to this chapter.)
 
Due Wednesday, Nov. 20, 11:59 pm: E-HW 17 Section 14.1
Due Monday, Nov. 25, 11:59 pm: E-HW 18 Section 14.2-14.3

Due Monday, Nov. 25: Writing Assignment 8: Job Offer

Quiz 11 Opportunity on Sections 13.3-13.4 for Wednesday, Nov. 20.
Wed., Nov. 20 Ellipses (14.3) Today's objectives:
1. Given the graph of an ellipse, report its formula in implicit and parametric form and other important properties.
 2. Given the implicitly defined formula of a hyperbola, report its formula in parametric form and other important properties.

 Do (for practice):
Flash Card 14.3 Ellipses: Given graph, report center, vertices, and formula
 Flash Card 14.4 Hyperbolas: Given implicitly defined formula, report center, vertices, etc.
If you have a text, see Section 14.4 -- 1-4, 15, 16 (See BB for a link to this chapter.)

Due tonight, Wednesday, Nov. 20, 11:59 pm: E-HW 17 Section 14.1
Due Monday, Nov. 25, 11:59 pm: E-HW 18 Section 14.2-14.3
Due Monday, Dec. 2, 11:59 pm: E-HW 19 Section 14.4

Due Monday, Nov. 25: Writing Assignment 8: Job Offer
Fri., Nov. 22 Hyperbolas (14.4) Today's objectives:
1. Given the graph of a hyperbola, report its formula in implicit and parametric form and other important properties.
 2. Given the implicitly defined formula of a hyperbola, report its formula in parametric form and other important properties.

Do (for practice):
Flash Card 14.4 Hyperbolas: Given implicitly defined formula, report center, vertices, etc.
Flash Card 14.4 Hyperbolas: Given graph, report center, vertices, and formula
If you have a text, see Section 14.4 -- 1-8, 15, 16 (See BB for a link to this chapter.) 

Due Monday, Nov. 25, 11:59 pm: E-HW 18 Section 14.2-14.3
Due Monday, Dec. 2, 11:59 pm: E-HW 19 Section 14.4

Due Monday, Nov. 25: Writing Assignment 8: Job Offer

 Alert: Quiz 12 Opportunity on Sections 14.1-14.3 (See eHW17 and eHW18) for Monday, Nov. 25.
Class meeting Topic Assignment
Monday,
Nov. 25		 Complex Numbers (9.6) Today's objectives:
1. Use notation for an imaginary number and complex number.
2. Plot a complex number on the complex plane.

Pythagoras would have liked this: https://www.ancient-code.com/nasa-has-discovered-that-stars-moons-and-planets-give-off-music-this-is-what-is-sounds-like/
However, he would not have liked this: https://curiosity.com/topics/pythagoras-may-have-been-a-murderous-math-cult-leader-curiosity/

Do (for practice):
If you have a text, see Section 9.6 -- 1-23, 27, 36-39

Due tonight, Monday, Nov. 25, 11:59 pm: E-HW 18 Section 14.2-14.3
Due Monday, Dec. 2, 11:59 pm: E-HW 19 Section 14.4
Alert: Quiz 13 Opportunity on Sections 14.4 (See eHW19) for Monday, Dec. 2.

Test 3 is available outside of class beginning Tuesday, Dec 3 up until Friday, Dec. 6
See Review Sheet. This is in the folder Reviews for Exams on Blackboard.
Wednesday,
Nov. 27		 No class meeting. Enjoy Thanksgiving Break!
Friday
Nov. 29		 No class meeting. Enjoy Thanksgiving Break!

What mathematicians say after a full Thanksgiving Dinner:
Class meeting Topic Assignment
Monday,
Dec. 2		 Complex Number Arithmetic (9.6) Today's objectives:
1. Perform arithmetic with complex numbers.
2. Represent a complex number as a vector.

Do (for practice):
If you have a text, see Section 9.6 -- 1-23, 27, 36-39

Due tonight, Monday, Dec. 2, 11:59 pm: E-HW 19 Section 14.4

Test 3 is available outside of class beginning Tuesday, Dec 3 up until Friday, Dec. 6
See Review Sheet. This is in the folder Reviews for Exams on Blackboard. A past recorded review session is posted in this BB folder.

No class meeting on Wed., Dec. 4
Need help?  Come to the classroom during our normal class meeting time and I will be there if you have questions.
I will also be in KT 123 from 11- noon.
Wednesday,
Dec. 4		 No class meeting. Take Test 3 in Math Test Center. However, you are welcome to come to KT 123 if you have any questions.
Friday
Dec. 6		 Why are Complex Numbers Important? (9.6)

Today's objective:
Work with complex numbers in polar form and exponential form.

Videos (all optional):
Complex numbers take us out of our three dimensional world. This video shows where the function f(x) = x2 + 1 has one of its zeros.
This video gives an entertaining history.
This video uses 3-D animations to show complex number arithmetic:
Here is one application involving AC circuits.

Do (for practice):
Flash Card 9.6 Complex Numbers - Given Rectangular, Write in Polar Form
Flash Card 9.6 Complex Numbers - Raise to a Power
Flash Card 9.6 Powers of i
 If you have a text, see Section 9.6 -- 1-23, 27, 36-39 and Chapter 9 Review --  13-16.

E-HW 20 Section 9.6 due 11:59 PM Friday, Dec. 13
Euler Extra Credit: Due the date of your final exam:

Rhino Opportunity for Late Assignments - Missed an assignment or want to improve your score on a past assignment? For each perfect score you earn before the due date in the "Assignments (for a Grade)" area, you may redo one assignment listed below at a 10% late penalty. All due 11:59 PM Sunday, Dec. 15.

Final Exam: (See review packet. Solutions are posted on Blackboard.)
9:00 Section:     Monday, Dec. 16 8:00 AM - 10:00 AM, KT 123
10:00 Section:   Wednesday, Dec. 18 8:00 AM - 10:00 AM, KT 123
(You may come to either one of these but if you come to the other section's time, please notify me in advance to see if there is room.)
Class meeting Topic Assignment
Monday,
Dec. 9		 Complex Number Arithmetic (9.6) - Raising to a Power

Today's objectives:
1. Raise i to a power.
2. Work with complex numbers in polar form and exponential form.

Do (for practice):
Flash Card 9.6 Complex Numbers - Raise to a Power
Flash Card 9.6 Powers of i
 If you have a text, see Section 9.6 -- 1-23, 27, 36-39 and Chapter 9 Review --  13-16.

E-HW 20 Section 9.6 due 11:59 PM Friday, Dec. 13
Euler Extra Credit: Due the date of your final exam.

Wednesday,
Dec. 11
 		 Review for the final exam E-HW 20 Section 9.6 due 11:59 PM Friday, Dec. 13
Euler Extra Credit: Due the date of your final exam.

QUIZ 14 Friday, Dec. 13 on 9.6
Rhino Opportunity for Late Assignments - Missed an assignment or want to improve your score on a past assignment? For each perfect score you earn before the due date in the "Assignments (for a Grade)" area, you may redo one assignment listed below at a 10% late penalty. All due 11:59 PM Sunday, Dec. 15.
Monday,
Dec. 13		 Review for the final exam E-HW 20 Section 9.6 due 11:59 PM Friday, Dec. 13
Euler Extra Credit: Due the date of your final exam.

Rhino Opportunity for Late Assignments - Missed an assignment or want to improve your score on a past assignment? For each perfect score you earn before the due date in the "Assignments (for a Grade)" area, you may redo one assignment listed below at a 10% late penalty. All due 11:59 PM Sunday, Dec. 15.

Final Exam: (See review packet. Solutions are posted on Blackboard.)
9:00 Section:     Monday, Dec. 16 8:00 AM - 10:00 AM, KT 123
10:00 Section:   Wednesday, Dec. 18 8:00 AM - 10:00 AM, KT 123
(You may come to either one of these but if you come to the other section's time, please notify me in advance to see if there is room.)

This page is on the Web at http://users.pfw.edu/lamaster/ma154/f19ma154.htm