FUNCTIONSp. 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
Core 2
A tachometer of a Ford Explorer reads 2,100 rpm at 60 rpm. Find the equivalent angular velocity in 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. / SFCC – Beginning & Intermediate Algebra
Not covered
SCC – Intermediate Algebra
Not in curriculum / Precalculus II

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

Core 1
Core 2
Determine the radian measures equivalent to the following degrees: 45, 150, 210
Determine the degree measures equivalent to the following radian measures. ,
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 / SFCC – Beginning & Intermediate Algebra
Not covered
SCC – Intermediate Algebra
Not in curriculum / Precalculus II

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
Core 2
Core 3
Integrated 3
Algebra 2, CPM
Algebra 2
Algebra 2/Trigonometry
Precalculus
Find the four remaining trigonometric functions of the angle given that and is in the 4th quadrant.
Memory Quizzes on the unit circle. / SFCC – Beginning & Intermediate Algebra
Not covered
SCC – Intermediate Algebra
Not in curriculum / Precalculus II

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

Core 1
Core 2
Core 3
Integrated 3
Algebra 2, CPM
Algebra 2
Algebra 2/Trigonometry
Precalculus
Graph the function

For each of the following, determine the amplitude, period and phase shift. / SFCC – Beginning & Intermediate Algebra
Not covered
SCC – Intermediate Algebra
Not in curriculum / Precalculus II

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
Core 2
Core 3
Integrated 3
Algebra 2, CPM
Algebra 2
Algebra 2/Trigonometry
Precalculus:
Write a cosine function 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. / SFCC – Beginning & Intermediate Algebra
Not covered
SCC – Intermediate Algebra
Not in curriculum / Precalculus II

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

Core 1
Core 2
Core 3
Integrated 3
Algebra 2, CPM
Algebra 2
Algebra 2/Trigonometry
Precalculus:
Given that and . Find each of the following exactly (be sure to simplify your answers):
(a)
(b)
(c) / SFCC – Beginning & Intermediate Algebra
Not covered
SCC – Intermediate Algebra
Not in curriculum / Precalculus II

g.Solve linear and quadratic equations involving trig functions.

Core 1
Core 2
Core 3
Integrated 3
Algebra 2, CPM
Algebra 2
Algebra 2/Trigonometry
Precalculus:
Solve the equation for ALLvalues of x. Provide exact answers in degrees or radians.
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)? / SFCC – Beginning & Intermediate Algebra
Not covered
SCC – Intermediate Algebra
Not in curriculum / Precalculus II

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

Core 1
Core 2
Core 3
Integrated 3
Algebra 2, CPM
Algebra 2
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 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. / SFCC – Beginning & Intermediate Algebra
Not covered
SCC – Intermediate Algebra
Not in curriculum / Precalculus II

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

Core 1
Core 2
Core 3
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 to do), the drive’s motor must adjust as you read 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 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 RiverfrontPark. 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. / SFCC – Beginning & Intermediate Algebra
Not covered
SCC – Intermediate Algebra
Not in curriculum / Precalculus II