precalculus resources emanual
DESCRIPTION
PreCalculus Resources eManualTRANSCRIPT
Lesson 1.1.1 Resource Page
76 Pre-Calculus with Trigonometry
Tubular Vision In this experiment, you will measure the diameter of the field of view as a function of your distance from the object (a wall). Materials: A tube, meter stick or a tape measure, and a ruler. Collecting the Data:
1. You will need the following roles for your group:
• A viewer (the one that will look through the tube) • A spotter (the one who will mark and measure on the board or wall the field of view) • A measurer (the one who measures the distance from the wall to the end of the tube) • A recorder
2. Measure a distance away from the wall to the end of the tube (the end away from the viewer eye) and record the distance. Stand facing the wall.
3. 4.
Instruct the spotter to make chalk (or pen marks if you are using paper) marks at the left and right edges of your field of view. Look straight ahead through the tube; do not roll your eyes. Use your peripheral vision to judge. Measure the distance (in cm) between the chalk marks. Then erase them to prepare for the next measurement.
><
Field of view looking through the tube.
5. Repeat steps 2 - 4 for different distances. Be sure to obtain eight data points. Record your results below:
Distance from Wall Field of View
Lesson 1.1.4 Resource Page Page 1 of 2
Chapter 1: Tools for Your Journey 77
Transformations of Graphs ONE STEP TRANSFORMATIONS Given the graph to the left, sketch the transformed graph to the right.
1. )2( !xf f(x)
2. )(2 xg!
g(x)
3.
�
h(x !1) + 3
)(xh
Lesson 1.1.4 Resource Page Page 2 of 2
78 Pre-Calculus with Trigonometry
MULTI-STEP TRANSFORMATIONS Given the graph to the left, sketch the transformed graphs to the right. Show each step of the two-step transformation. 4.
�
k(x) = 3 f (x) +1 5.
�
m(x) = !2 f (x !1) 6.
�
p(x) =12f (x) + 3
7.
�
q(x) =12f (x ! 2)
f(x)
f(x)
f(x)
f(x)
Lesson 1.2.2A Resource Page
Chapter 1: Tools for Your Journey 79
Quadratic Formula—TI-83/84
STEPS DISPLAY Select , then select NEW EXEC EDIT
Create New
NEW
1: Press Í
Type QUADFORM and press Í
PROGRAM: QUADFORM :
Press then select I/O Select 8 then press Í This command will clear the screen at the start of the program.
PROGRAM: QUADFORM :ClrHome
Input
Select and arrow over to I/O. Select 1: (Input). To get the quote, push ƒ then . Press ƒ will give the A. Press y
[TEST] and choose = . Press ƒ then again to end the quote. Press ¢ (found above ¬). Use ƒ again and select A. Repeat the same steps so B and C can be inputted.
PROGRAM: QUADFORM : ClrHome :Input "A=", A
Process
These variables are obtained by using the ƒ key. We want to rename B2 – 4AC as D. To store this new quantity into memory, we use the ¿ key followed byƒ—[D].
:B2 – 4AC→D
We need to do two more calculations, one for each root. Enter the line (-B+√(D))/(2A)→R into the program. Write another line that will calculate the second root and store the result into S.
Output
The Disp is found as before. Note that the R and S do not have quotes around them.
:Disp R :Disp S
Select yz 5to exit the program.
+
+
Lesson 1.2.2B Resource Page
80 Pre-Calculus with Trigonometry
Sierpinski’s Triangle 1. Choose any point inside the triangle. 2. Roll a die to randomly pick a vertex, A, B, or C. If the result is a 1 or 2, find the
midpoint that goes toward A. If the result is a 3 or 4, find the midpoint that goes toward B. If the result is a 5 or 6, find the midpoint that goes toward C.
3. Plot the midpoint between the point from part 1 and the vertex from part 2. 4. Using the point you created in part 3, repeat steps 2 and 3 at least 6 times.
C
B A
Lesson 1.4.2 Resource Page
Chapter 1: Tools for Your Journey 81
Angles in a Unit Circle
0
Chapter 1 Closure Resource Page: Key Ideas
82 Pre-Calculus with Trigonometry
Function Definition
Domain and Range
Parent Graphs
Transformations: Shifting and Stretching Functions
Working with Exponents (Including Negative and Fractional)
Inverse of a Function
Operations with Functions
Transformations of Non-Parent Functions
Point-Slope Form of a Line
Law of Sines and Law of Cosines
Special Triangles
Radians: Measuring Angles in the Unit Circle
Key Ideas Ideas Chapter 1
Lesson 2.1.2A Resource Page
174 Pre-Calculus with Trigonometry
!"#
=___________
___________)(xh
B.
D.
SHIFTING GRAPHS
�
k(x) =___________
___________
!
"
#
A.
C.
Lesson 2.1.2B Resource Page
Chapter 2: Finding the Area Under a Curve 175
Periodic Functions
10 8 6 4 2 -4 -2
(1, 4) (6, 4)
(5, 2)
Lesson 2.2.2 Resource Page
Sum Formula—TI-83/84
STEPS DISPLAY Select , then select NEW EXEC EDIT
Create NewNEW
1: Press Í
Type SUM and press Í
PROGRAM: SUM :
Press then select I/O Select 8 then press Í This command will clear the screen at the start of the program.
PROGRAM: SUM :ClrHome
Input
Press ¿ ƒ µ Í. Press ¿ „ Í.
PROGRAM: SUM : ClrHome : 0 → S : 1 → X
Process
Select and scroll down to 9: Lbl Press Í and then  Í
Press ƒ µ To get the Y1, press , arrow over to Y-VARS, select 1:FUNCTION and press Í Press „ ¿ „ Í
Select and then select 1: If (press Í) Press „ y ¸, then type · Í
Select and scroll down to 0: Goto Press Í and then  Í
: Lbl 3 : S + Y1 → S : X + 1 → X : If X ≤ 5 : Goto 3
Output
Select and arrow over to I/O. Select 3: Disp Press ƒ µ
:Disp S
Select y z 5to exit the program. Before running the program, be sure that you have a function entered in Y1.
¥
¥
Lesson 2.3.1 Resource Page
176 Pre-Calculus with Trigonometry
Area Under a Curve – Part I 2-64. 2-65.
Chapter 2 Closure Resource Page: Key Ideas
Chapter 2: Finding the Area Under a Curve 177
Piecewise Functions
Intuitive Notion of Continuity
Horizontal and Vertical Shifts of Piecewise Functions
Periodic Functions
Sigma Notation
Estimating Area Under a Curve with:
– Left-Endpoint Rectangles
– Right-Endpoint Rectangles
– Trapezoids
– Midpoint Rectangles
Shifting Areas
Area as a Function
Key Ideas Ideas Chapter 2
Lesson 3.1.1 Resource Page
Chapter 3: Exponentials and Logs 247
3-5. a. 2 f (x) b. f (2x) c. ! f (x) d. f (!x)
f (x)
f (x)
f (x)
f (x)
Chapter 3 Closure Resource Page: Key Ideas
248 Pre-Calculus with Trigonometry
kf(x) and f(kx) Transformations
Applications of Exponential Functions
Equivalent Transformations
Inverse Functions
– Vertical Line Test
– “Switch and Solve” method
Definition of Logarithm
Log Graphs
Laws of Logarithms
Solving Exponential and Logarithmic Equations
LN vs. LOG
Key Ideas Ideas Chapter 3
Lesson 4.1.1A Resource Page
322 Pre-Calculus with Trigonometry
UNIT CIRCLE AND SPECIAL TRIANGLES
!
Lesson 4.1.1B Resource Page
Chapter 4: Circular Functions 323
�
32
�
2
2
�
!3
�
!4
�
!6
�
!2
�
1
2
�
1
2
�
2
2
�
32
�
!"6
�
!"4
�
!"3
�
!"2
-1
-1
.5
-.5
Lesson 4.1.1C Resource Page
324 Pre-Calculus with Trigonometry
Unit Circle
!6
3
2, 1
2( )π/6
!4
2
2,
2
2( )
!3
1
2,
3
2( )
!2
0,1( ) !
1
2,
3
2( ) 2"3
!2
2,
2
2( ) 3"4
!3
2, 1
2( ) 5"6
!1, 0( ) "
!3
2, ! 1
2( ) 7"6
!2
2, !
2
2( ) 5"4
!1
2, !
3
2( ) 4"3 3!2
0, "1( )
5!3
12
, "3
2( )
7!4
2
2, "
2
2( )
0 1, 0( )
11!6
3
2, " 1
2( )
(+ , +) (+ , –)
(– , –)
(– , +)
Lesson 4.1.3A Resource Page
Chapter 4: Circular Functions 325
Building a Sine Curve
π/6
π/4
π/3 π/2
2π/3
3π/4
5π/6
π
7π/6
5π/4 4π/3
3π/2 5π/3
7π/4
0, 2π
11π/6
Cut
Off
Lesson 4.1.3B Resource Page
326 Pre-Calculus with Trigonometry
y =
sinθ
y =
cosθ
Lesson 4.1.4 Resource Page
Chapter 4: Circular Functions 327
Trig Graphs
Lesson 4.1.4 Resource Page
328 Pre-Calculus with Trigonometry
Trig Graphs
Lesson 4.3.2A Resource Page
Chapter 4: Circular Functions 329
sin x
cos x
y = sin x + cos x
Lesson 4.3.2B Resource Page
330 Pre-Calculus with Trigonometry
y = x + sin(x)
Chapter 4 Closure Resource Page
354 Pre-Calculus with Trigonometry
GRAPHICAL REPRESENTATION OF TRIG FUNCTIONS
P
A
C
B
θ D
1
Chapter 4 Closure Resource Page: Key Ideas
Chapter 4: Circular Functions 353
Angles and Coordinates in the Unit Circle
Sine and Cosine in the Unit Circle
The Fundamental Pythagorean Identity
Using Right Triangles to Find Trigonometric Ratios
Graphs and Transformations of Sine and Cosine
The Five-Point Method for Graphing Sine and Cosine
The Reciprocal Trig Functions
Other Trigonometric Functions in the Unit Circle
Simplifying Complex Fractions
Angular Frequency and Period
The General Sine Function
The Three Pythagorean Identities
Verifying Identities
Modeling with Periodic Functions
Graphical Addition
Key Ideas Ideas Chapter 4
Lesson 5.1.1 Resource Page
406 Pre-Calculus with Trigonometry
View Tube Revisited
Name:_______________
Your group’s distance from the wall:__________
Tube Tube length (cm) View diameter (cm) A B C D E F G H
Sketch your stat plot here: Observations and conclusions:
Lesson 5.1.3 Resource Page
Chapter 5: Introduction to Limits 407
Graphs of Secant and Cosecant
The graph of f (x) = cos x is shown below. Use this graph to sketch 1
f (x)= sec x .
The graph of f (x) = sin x is shown below. Use this graph to sketch 1
f (x)= csc x .
2! !"
2 !"
!3"
2 !2"
1
2
3
4
–1
–2
–3
–4
!
2 ! 3!
2
y
x
2! !"
2 !"
!3"
2 !2"
1
2
3
4
–1
–2
–3
–4
!
2 ! 3!
2
y
x
Chapter 5 Closure Resource Page: Key Ideas
408 Pre-Calculus with Trigonometry
Direct and Inverse Variations
Transforming Rational Functions
Simplifying Algebraic Fractions
Graphing
�
1
f (x)
Definition of a Limit
One-Sided Limits
Continuous Function
Piecewise Functions and Limits
Key Ideas Ideas Chapter 5
Lesson 6.1.2 Resource Page
482 Pre-Calculus with Trigonometry
Inverse Sine Inverse Cosine
π 2π –π –2π
π
2π
–π
–2π
x
y
π 2π –π –2π
π
2π
–π
–2π
x
y
Lesson 6.1.4 Resource Page
Chapter 6: Extending Periodic Functions 483
Tangent Graph (cosine provided for reference)
Inverse Tangent
Lesson 6.2.3 Resource Page
484 Pre-Calculus with Trigonometry
Trig Modeling Resource Page
PROBLEM RELEVANT INFORMATION EQUATION and SKETCH 1 Period
Number of cycles in 2π Amplitude Vertical Shift Horizontal Shift
2 Period Number of cycles in 2π Amplitude Vertical Shift Horizontal Shift
3 Period Number of cycles in 2π Amplitude Vertical Shift Horizontal Shift
4 Period Number of cycles in 2π Amplitude Vertical Shift Horizontal Shift
5 Period Number of cycles in 2π Amplitude Vertical Shift Horizontal Shift
6 Period Number of cycles in 2π Amplitude Vertical Shift Horizontal Shift
7 Period Number of cycles in 2π Amplitude Vertical Shift Horizontal Shift
8 Period Number of cycles in 2π Amplitude Vertical Shift Horizontal Shift
9 Period Number of cycles in 2π Amplitude Vertical Shift Horizontal Shift
Lesson 6.4.1 Resource Page Page 1 of 2
Chapter 6: Extending Periodic Functions 485
The Spring Problem Materials Each group will need the following: • One Slinky Jr. • Clay (or play dough) to act as a weight • A meter stick or other measuring device ( butcher paper marked every 2 cm) • A stop watch Tasks for the team: Holder: The person who holds the slinky in place. Timer: The person who times the period of an oscillation. Low Spotter: The person who spots the lowest position. High Spotter: The person who spots the highest position. 1. Attach the clay to the end of the slinky. 2. The holder should hold the non-clay end of the slinky
and extend his/her arm out so that it can be held steady for a period of time. Holding the top against a door or window jamb will make this easier. You will need to hold about
�
1
4 of the coils from the top.
Separate this section by using a ruler or other thin flat object, as shown in the picture to the right.
3.
Allow the slinky to hang loose so that you get an idea of the middle position during the oscillations. Adjust the number of coils above the ruler if the spring hangs too low. The upper spotter should raise the clay between 20 and 30 cm above the center position. The measurements will go as follows: DROP LOW POINT HIGHT POINT LOW POINT HIGH POINT -- Mark here LOW POINT -- Mark here HIGH POINT -- Mark again
Practice a couple of test drops to get an idea of the high and low positions. Once you have established your standards you are ready to begin the experiment. 4. Draw a line on the paper or use the floor as a reference point to measure from.
Lesson 6.4.1 Resource Page Page 2 of 2
486 Pre-Calculus with Trigonometry
Team Task:
Holder: To keep your arm and hand steady to avoid any secondary motion.
Spotters: The high spotter is in charge of dropping the clay. Make a mark at the starting position so that each trial will start from the same point. Once the motion has started, mark the low and high points of the clay on the paper as specified previously. Use different colors or numbers for each trial.
Timer: Start the stop watch when the weight hits its the high marking point. Stop the watch when it reaches its next high point.
PART 1: Run the experiment three times. Record your data on the chart below. All heights are measured from the reference line or floor.
TRIAL 1 TRIAL 2 TRIAL 3 MEAN
FIRST HIGH POINT
LOW POINT
SECOND HIGH POINT
TIME
PART 2: In this part we wish to concentrate on the period of an oscillation. Measure the time it takes for the spring to make the specified number of oscillations. If you have more than one stop watch you can speed up the process. Choose a dropping height similar to the one you used in Part 1. An approximation is fine here since we are only concerned about the timing. Start timing after one or two oscillations to minimize the effects of secondary motion. To calculate the period, divide the time by the number of oscillations. We will sketch a graph of the motion during our analysis. To help develop the graph, the spotters should pay close attention to the motion of the slinky and record their observations. Complete the chart below:
Oscillations 2 4 6 8 10 20
Time
Period
Chapter 6 Closure Resource Page: Key Ideas
Chapter 6: Extending Periodic Functions 487
Solving Trig Equations
Inverse Sine and Inverse Cosine
Ambiguous Case for the Law of Sines
Tangent and Inverse Tangent
Graphing Trig Functions of the Form
�
y = asin(b(x ! h)) + k
Angle Sum and Difference Formulas
Modeling With Trig Functions
Double and Half Angle Formulas
Solving Complex Trig Equations
Key Ideas Ideas Chapter 6
Lesson 7.1.2 Resource Page Page 1 of 2
554 Pre-Calculus with Trigonometry
ODD AND EVEN FUNCTIONS
Fill in the table below for the following power functions. Why are they called power functions? How are they different from exponential functions? In the column labeled “symmetry,” record whether they are symmetric about the x-axis, the y-axis, the origin, or none of these.
Equation Sketch f (!x) f (!x) Simplified Symmetry
�
f (x) = x4
�
f (x) = x2
�
f (x) = x0
�
f (x) = x!2
�
f (x) = x!4
a. Why might these functions be called “even?”
b. Write an identity describing the relationship between
�
f (!x) and
�
f (x) in all cases. f (!x) = ?
c. Describe the symmetry of the graphs of these “even” functions.
A function
�
f (x) is called an EVEN FUNCTION if, for all x,
�
f (!x) =
�
f (x) .
d. In your study teams, come up with at least one other function that is even other than using even integer exponents. Think symmetry!
Lesson 7.1.2 Resource Page Page 2 of 2
Chapter 7: Algebra for College Mathematics 555
Fill in the table below for the following power functions.
Equation Sketch f (!x) f (!x) Simplified Symmetry
�
f (x) = x5
�
f (x) = x3
�
f (x) = x1
�
f (x) = x!1
�
f (x) = x!3
a. Why might these functions be called “odd?”
b. Write an identity describing the relationship between
�
f (!x) and
�
f (x) in all cases. f (!x) = ?
c. Describe the symmetry of the graphs of these “odd” functions.
A function
�
f (x) is called an ODD FUNCTION if, for all x,
�
f (!x) = –
�
f (x) .
d. In your group come up with at least one other function that is odd, other than using odd exponents. Think symmetry!
Lesson 7.2.3 Resource Page
556 Pre-Calculus with Trigonometry
Polynomial Division
Fill in the generic rectangles to complete the multiplication of the terms. State the resulting product. a. (x ! 3)(2x3 + x2 ! 2x +1) b. (2x +1)(x3 + 2x2 ! 3)
�
___ x4_____ x
3______ x
2_____ x ______
�
___ x4_____ x
3______ x
2_____ x ______
Use the generic rectangles to find the following quotients: c. (x4 ! x3 ! 4x2 + 8x + 8) ÷ (x + 2) d. (4x3 + 4x2 ! 7x ! 6) ÷ (2x + 3) x4
! x3
! 4x2
+ 8x + 8 4x3
+ 4x2
! 7x ! 6 What if it does not divide completely? The examples below show two methods for dividing, both have remainders that we write as fractions.
x4! 6x
3+18x !1
x ! 2
Using Long division:
x ! 2 x4! 6x
3+ 0x
2+18x !1
x4! 2x
3
! 4x3+ 0x
2
! 4x3+ 8x
2
! 8x2+18x
! 8x2+16x
2x !1
2x ! 4
3
x3! 4x
2! 8x + 2
Final Answer: x3 ! 4x2 ! 8x + 2 + 3
x!2
Using Generic Rectangles: x4! 6x
3+ 0x
2+18x !1
Final Answer: x3 ! 4x2 ! 8x + 2 + 3
x!2
x3 !4x
2 !8x +2
x x4 !4x
3 !8x2 + 2x 3
–2 !2x3 +8x
2 + 16x –4
Remainder
2x3 +x
2 !2x +1
x
–3
x3 +2x
2 +0x !3
2x
+1
x x4
+2
2x 4x3
+3
Remainder
Lesson 7.2.4 Resource Page
Chapter 7: Algebra for College Mathematics 557
Pascal’s Triangle Fill in the appropriate values below.
Row 0
Row 1
Row 2
Row 3
Row 4
Row 5
Row 6
Chapter 7 Closure Resource Page: Key Ideas
558 Pre-Calculus with Trigonometry
Properties of Functions
– Increasing and Decreasing Functions
– Concavity
– Even and Odd Functions
Setting up Word Problems
Simplifying Algebraic Expressions
Using Substitution
Completing the Square
Polynomial Division
Addition of Series
– Arithmetic Series
– Geometric Series
Pascal’s Triangle
– Binomial Expressions
– Binomial Probabilities
Key Ideas Ideas Chapter 7
Lesson 8.1.1 Resource Page
628 Pre-Calculus with Trigonometry
RACE TO INFINITY
Contestants:
�
a(x) = 50 x
�
e(x) = 2x!1000
�
b(x) = x10
�
f (x) = x
�
c(x) =100x2
�
g(x) =1.1x
�
d(x) = 800log x
�
h(x) = 20x3
Listed above are several functions which all go to infinity as x gets large. Your team’s task is to determine the order of the finish. You will need to figure out which one moves to infinity the quickest as x gets large. In other words, you will determine which function “dominates” the others. Use the chart below to help determine the order of the functions for various values of x. You will need to use scientific notation for several of the entries.
Function x = 1 x = 10 x = 100 x = ??
�
a(x) = 50 x
�
b(x) = x10
�
c(x) =100x2
�
d(x) = 800log x
�
e(x) = 2x!1000
�
f (x) = x
�
g(x) =1.1x
�
h(x) = 20x3
a. What is the order of the functions when x = 1?
b. What is the order of the functions when x = 10?
c. What is the order of the functions when x = 100?
d. What is the final order of finish?
e. Challenge: At what point (value for x) will the order no longer change? Which functions change position at this point?
Lesson 8.1.4 Resource Page
Chapter 8: More on Limits 629
Finding the Area of a Circle 8-48. First the area of the inscribed dodecagon.
a. What is the central angle of each of the isosceles triangle shown?
b. Given the radius is one unit, what is the height of one of the isosceles triangles. Do not find the decimal approximation.
c. What is the base of each isosceles triangle? Do not find the decimal approximation.
d. Find the area of the inscribed polygon. 8-49. Now find the area of the circumscribed
dodecagon.
a. What is the base of each isosceles triangle? Do not find the decimal approximation?
b. Given the height of each triangle is one unit. Find the area of the polygon.
Use the diagrams below to assist you with problems 8-50 and 8-52. 8-50. 8-52.
1
1
Chapter 8 Closure Resource Page: Key Ideas
630 Pre-Calculus with Trigonometry
Dominant Terms
Limits to Infinity
Holes and Asymptotes
Squeeze Method
The Number e
�
ex and
�
ln x
Pert and Applications of e
Infinite Geometric Series
The Harmonic Series
The Fibonacci Series
Key Ideas Ideas Chapter 8
Lesson 9.2.2 Resource Page
708 Pre-Calculus with Trigonometry
�
g(x) = 3x +1
14)( 2++!= xxxf
Lesson 9.3.1 Resource Page
Chapter 9: Rates of Change 709
Resource Page: Scenario 1
1. Walk slowly at a constant speed from “start” for 10 seconds.
2. Stop for 5 seconds.
3. Walk slowly again for 5 seconds.
4. Stop for 5 seconds.
5. Run towards “finish” for 5 seconds. -------------------------------------------------------------------------------------------------------------------------------------- Lesson 9.3.2 Resource Page
Resource page: Scenario 2
1. Walk slowly from “start” for 10 seconds.
2. Stop for 5 seconds.
3. Walk slowly back towards “start” for 5 seconds.
4. Stop for 5 seconds.
5. Run towards “finish” for 5 seconds.
Chapter 9 Closure Resource Page: Key Ideas
710 Pre-Calculus with Trigonometry
Rates of Change
Slope and Rates of Change
Average Rate of Change: AROC
Instantaneous Rate of Change: IROC
Secant Line vs. Tangent Line
Velocity and Position Graphs
Definition of a Derivative
Slope of a Function and Area Under a Curve
Key Ideas Ideas Chapter 9
Lesson 10.1.1 Resource Page
Chapter 10: Vectors and Parametric Equations 767
Vector Line Dance
Step Move Vector Angle and Magnitude
Sketch
1 Right 2 2, 0 0°, 2
2 Up 1 0, 1
3 Back 2 0, ! 2
4 Up 1, Left 1 !1, 1 135°,
�
2
5 Left 2
6 Up 1, Right 1 1, 1
7 Down 1, Right 1
Chapter 10 Closure Resource Page: Merge Problem
768 Pre-Calculus with Trigonometry
Math Magic Land – Spinning Cups One of the most popular rides at Math Magic Land is the Spinning Cups. During the ride, the large outer disk rotates counter-clockwise and makes a complete revolution every 30 seconds. The medium size disk rotate clockwise every 4 seconds. The passenger can rotate the smallest disk (the cup) counter-clockwise as fast as they want. Janelle (labeled as J) loves making her friends dizzy on the ride. When she rides, she spins the cup one full turn every two seconds. The main disc has a radius of 100 feet. The medium disc has a radius of 40 feet and the cups each have a radius of 4 feet.
100 ft 40 ft
4 ft
30 ft
50 ft
J
M
Chapter 10 Closure Resource Page: Key Ideas
Chapter 10: Vectors and Parametric Equations 769
Vector Addition
Magnitude and Standard Angle of a Vector
Component Form of a Vector
Unit Vectors
Applications of Vectors
Dot Product
Parametric Equations
Vector Equations
Inverses and Parametric Equations
Applications of Parametric Equations
Key Ideas Ideas Chapter 10
Lesson 11.1.1 Resource Page: Polar Graph Paper
Chapter 11: Polar Coordinates and Complex Numbers 811
Polar Graph Paper
Ch 10 Closure Resource Page: Key Ideas
812 Pre-Calculus with Trigonometry
Polar Coordinates
Conversions Between Polar and Rectangular Forms
Polar Graphs: Common Forms, Rotations
Complex numbers: Simplifying, Graphing
Polar Form of Complex numbers
Multiplying and Dividing Complex Numbers
Powers and Roots of Complex Numbers
DeMoivre’s Theorem
Key Ideas Ideas Chapter 11
Chapter 12 Closure Resource Page: Key Ideas
Chapter 12: Linear Transformations 851
Matrices
Matrix Operations (adding, multiplying)
Identity Matrix
Inverse Matrix
Linear Transformation
Rotation Matrix
Vectors and Matrices
Composition of Matrices
Eigenvalues
Key Ideas Ideas Chapter 12