# Algebra Standard

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```					FUNCTIONS                                                                                                                                               p. 1

8.6 Recognize, analyze, interpret, and model with trigonometric functions.

High School                                         Community College                                               EWU

a. Represent and interpret trig functions using the unit circle.

Core 1                                                    SFCC – Beginning & Intermediate Algebra                Precalculus II
Not covered

Core 2
A tachometer of a Ford Explorer reads 2,100 rpm at        SCC – Intermediate Algebra
60 rpm. Find the equivalent angular velocity in           Not in curriculum
degrees per minute and in radians per minute.
The idle speed of a Ford Explorer is 1,000 rpm. Find
the angular velocity in radians per minute.

Core 3

Integrated 3

Algebra 2, CPM

Algebra 2

Algebra 2/Trigonometry

Precalculus:
Memory Quizzes on the unit circle.

b. Demonstrate an understanding of radians and degrees by converting between units, finding areas of sectors, and determining arc lengths of circles.

Core 1                                                    SFCC – Beginning & Intermediate Algebra                Precalculus II
Not covered

Core 2
Determine the radian measures equivalent to the           SCC – Intermediate Algebra
following degrees: 45, 150, 210                        Not in curriculum
FUNCTIONS                                                                                                                                                                  p. 2

8.6 Recognize, analyze, interpret, and model with trigonometric functions.

High School                                         Community College                                                  EWU

Determine the degree measures equivalent to the
    11
6     6

Core 3

Integrated 3

Algebra 2, CPM

Algebra 2

Algebra 2/Trigonometry

Precalculus
Convert to radians, convert to degrees.

Find the arc length.

Find the area of the sector

c. Find exact values (without technology) of sine, cosine and tangent for unit circle and for multiples of π / 6 and π / 4; evaluate trigonometric ratios; and distinguish between
exact and approximate values when evaluating trig ratios/functions.

Core 1                                                   SFCC – Beginning & Intermediate Algebra                    Precalculus II
Not covered

Core 2
SCC – Intermediate Algebra
Not in curriculum
Core 3
FUNCTIONS                                                                                                                                    p. 3

8.6 Recognize, analyze, interpret, and model with trigonometric functions.

High School                                           Community College                                           EWU

Integrated 3

Algebra 2, CPM

Algebra 2

Algebra 2/Trigonometry

Precalculus
Find the four remaining trigonometric functions of
5
the angle  given that sin      and  is in the 4th
13

Memory Quizzes on the unit circle.

d. Sketch graphs of sine, cosine, and tangent functions, without technology; identify the domain, range, intercepts, and asymptotes.

Core 1                                                  SFCC – Beginning & Intermediate Algebra                   Precalculus II
Not covered

Core 2
SCC – Intermediate Algebra
Not in curriculum
Core 3

Integrated 3

Algebra 2, CPM
FUNCTIONS                                                                                                                                                               p. 4

8.6 Recognize, analyze, interpret, and model with trigonometric functions.

High School                                           Community College                                                 EWU

Algebra 2

Algebra 2/Trigonometry

Precalculus
Graph the function
    
f ( x)  2 cos x  
    3

For each of the following, determine the amplitude,
period and phase shift. f x   sin 2 x  6c 
a
b

e. Use transformations (horizontal and vertical shifts, reflections about axes, period and amplitude changes) to create new trig functions (algebraic, tabular, and graphical).

Core 1                                                  SFCC – Beginning & Intermediate Algebra                    Precalculus II
Not covered

Core 2
SCC – Intermediate Algebra
Not in curriculum
Core 3

Integrated 3

Algebra 2, CPM

Algebra 2

Algebra 2/Trigonometry
FUNCTIONS                                                                                                                                  p. 5

8.6 Recognize, analyze, interpret, and model with trigonometric functions.

High School                                          Community College                                         EWU

Precalculus:
Write a cosine function f x  that has an amplitude
of 1, period of 31 and phase shift of 2003 to the
right.

The following are sunset times by month for
Spokane, WA. Daylight savings is ignored. The
sunset time is given in minutes after noon.
Furthermore, the times are for January 1, February 1,
March 1, etc.
Month          Sunset       Month        Sunset
1            248           7             471
2            290           8             444
3            334           9             391
4            379           10            329
5            422           11            272
6            460           12            240
Find a good model using a sine curve. Be sure to
explain vertical shift, amplitude, period, and phase
shift.

f. Know and apply the identity co²s x + sin² x = 1 and generate related identities; apply sum and half-angle identities.

Core 1                                                  SFCC – Beginning & Intermediate Algebra                    Precalculus II
Not covered

Core 2
SCC – Intermediate Algebra
Not in curriculum
Core 3

Integrated 3
FUNCTIONS                                                                                                                 p. 6

8.6 Recognize, analyze, interpret, and model with trigonometric functions.

High School                                        Community College                          EWU

Algebra 2, CPM

Algebra 2

Algebra 2/Trigonometry

Precalculus:
4                 3
Given that tan       and           . Find each
3                  2
of the following exactly (be sure to simplify your
(a) sin 2 
(b) cos2 
 
(c) tan 
2

g. Solve linear and quadratic equations involving trig functions.

Core 1                                                  SFCC – Beginning & Intermediate Algebra   Precalculus II
Not covered

Core 2
SCC – Intermediate Algebra
Not in curriculum
Core 3

Integrated 3

Algebra 2, CPM

Algebra 2
FUNCTIONS                                                                                                                                      p. 7

8.6 Recognize, analyze, interpret, and model with trigonometric functions.

High School                                          Community College                                            EWU

Algebra 2/Trigonometry

Precalculus:
Solve the equation
2 sin x cos x  sin 2 xcos 2 x   0 for ALL values of

A planter in the shape of a trapezoidal prism is being
constructed. The base should be 1 foot long by 2
feet wide and the top should be 1½ feet long.
However, I don’t know how tall I want it to be. I
figure it should probably hold between 4 and 10
cubic feet of soil. What range of angles should the
edge project out at (to the nearest minute)? How
deep will the planter be (to the nearest tenth of a
foot)?

h. Generate algebraic and graphical representation of inverse trig functions (arcsin, arccos, arctan), and determine domain and range.

Core 1                                                      SFCC – Beginning & Intermediate Algebra             Precalculus II
Not covered

Core 2
SCC – Intermediate Algebra
Not in curriculum
Core 3

Integrated 3

Algebra 2, CPM

Algebra 2
FUNCTIONS                                                                                                                      p. 8

8.6 Recognize, analyze, interpret, and model with trigonometric functions.

High School                                           Community College                           EWU

Algebra 2/Trigonometry

Precalculus:
The Follger Film Company is filming Michelle’s
model rocket launch. The lead filmmaker, Whitney,
programs the camera to automatically track the
rocket during its flight. The camera is on the ground
100 feet from the rocket. Let ß be the angle of
elevation from the camera to the shuttle. Let
ht   280t  16t 2 represent the rocket’s height (feet)
given time (seconds).
(a) Find a function ß(h) where h is the rocket’s
height in feet and describe what it represents.
(b) Find a function ß(t) where t is time in seconds
and describe what it represents.
(c) Find the domain and range of ß(t). Explain their
meaning in context.
(d) Graph ß(t) over the domain and explain what it
means.
(e) Find the camera’s angle when the rocket’s
height is 150 ft. Round to the nearest degree.
(f) Find the camera’s angle after 2 seconds. Round
to the nearest degree.

i. Use trig and inverse trig functions to solve application problems.

Core 1                                                       SFCC – Beginning & Intermediate Algebra   Precalculus II
Not covered

Core 2
SCC – Intermediate Algebra
Not in curriculum
Core 3
FUNCTIONS                                                                                          p. 9

8.6 Recognize, analyze, interpret, and model with trigonometric functions.

High School                                        Community College   EWU

Integrated 3

Algebra 2, CPM

Algebra 2

Algebra 2/Trigonometry

Precalculus:
Biorythms are mathematically based predictors of
your physical, emotional, and intellectual capabilities
(in terms of a percentage) for a given day. The
physical cycle is 23 days in length, the emotional
cycle is 28 days in length, and the intellectual cycle
is 33 days in length. On the day of your birth, each
cycle (which follows a sine/cosine curve) is at 50%
and decreasing.
(a) Leonhard Euler was born on April 15, 1707. He
died of a stroke on September 18, 1783.
Determine Euler’s best physical, emotional,
intellectual, and overall day in the month of
September 1783.
(b) How was his physical day on the day he died?
(c) Construct a chart of your overall biorythm
(combine the three) for the month of February
2004.

A typical CD’s data ranges from an inner radius of
2.25 cm to an outer radius of 5.5 cm. If a CD player
is to read the data at a constant rate (which they used
from the different parts of the CD. The motor’s
maximum speed is 10000 revolutions per minute.
(a) Find the angular (in radians/minute) and linear
(in meters/second) velocity at the outermost
FUNCTIONS                                                                                          p. 10

8.6 Recognize, analyze, interpret, and model with trigonometric functions.

High School                                        Community College   EWU

point of the CD.
(b) Find the angular (in radians/minute) and linear
(in meters/second) velocity at the innermost
point of the CD.
(c) Define the motor’s speed (in revolutions/second)
as a function of the radius of the CD. Clearly
identify units, discuss domain and range, and
include an appropriate graph.

A new Ferris wheel (in honor of the best school in
Spokane) is being put in at Riverfront Park. The
maximum height needs to be 150 feet above the
ground so riders can see over the neighboring pine
trees. The platform to get on the ride will sit 10 feet
above the ground. Once everyone is on the ride, the
wheel will make one leisurely revolution in two
minutes. Construct a function to model a rider's
height above the ground. Be sure to include
appropriate sketches and define all variables.

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