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Precalculus
Trigonometric Functions

1
Angles and Their Measure

Problem  1
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Sketch each of the following angles in standard position.

a. 120\(^{\circ}\)

b. \(-45\)\(^{\circ}\)

c. 450\(^{\circ}\)

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Nathan
Nathan
Molly S. cc
Molly S.
Ryan
Ryan
Problem  2

For each angle, find two angles that are coterminal with it.

a. 135\(^{\circ}\) b. \(-60\) \(^{\circ}\)

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Tim
Tim
Molly S. cc
Molly S.
Ryan
Ryan
Julieta cc espanol spanish
Julieta
Problem  3
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a. Find the complement of a 63\(^{\circ}\) angle.

b. Find the complement of a 105\(^{\circ}\) angle.

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Tim
Tim
Molly S. cc
Molly S.
Ryan
Ryan
Julieta cc espanol spanish
Julieta
Problem  4
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Convert each angle from degrees to radians.

a. 225\(^{\circ}\)

b. 60\(^{\circ}\)

c. –135\(^{\circ}\)

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Tim
Tim
Molly S. cc
Molly S.
Ryan
Ryan
Julieta cc espanol spanish
Julieta
Problem  5
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Tim
Tim
Molly S. cc
Molly S.
Ryan
Ryan
Julieta cc espanol spanish
Julieta
Problem  6
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Find the length of an arc of a circle of a radious 3 inches that is cut off by an angle of \(\displaystyle\frac{\pi}{6}\) radians.

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Tim
Tim
Molly S. cc
Molly S.
Ryan
Ryan
Julieta cc espanol spanish
Julieta
Problem  7
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Find the distance traversed by the tip of the second hand on a clock as it moves from the 0-second mark to the 20-second mark. The length of the second hand is 5 inches.

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Tim
Tim
Molly S. cc
Molly S.
Ryan
Ryan
Julieta cc espanol spanish
Julieta
Problem  8

A vintage vinyl record makes 45 revolutions per minute. What is the linear speed of point 3 inches from the center? See Fuigure 17.

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Saba cc
Saba
Molly S. cc
Molly S.
Gordon cc
Gordon
Julieta cc espanol spanish
Julieta
Problem  9

In a bicycle race, on of the bicyclists travels at a speed of 40 kilometers per hour. If the diameter of the bicycle wheel is 0.66 meters, find the angular speed of the wheel in

a. radians per hour.

b. revolutions per hour.

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Saba cc
Saba
Molly S. cc
Molly S.
Gordon cc
Gordon
Julieta cc espanol spanish
Julieta

2
Trigonometric Functions Using the Unit Circle

Problem  1

Find the sine and cosine of the following angle

a. t = 0

b. t = \(\displaystyle\frac{3\pi}{2}\)

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Saba cc
Saba
Nathan
Nathan
Julieta cc espanol spanish
Julieta
Problem  2
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Mr. Hampton
Mr. Hampton
Penelope
Penelope
Nathan
Nathan
Julieta cc espanol spanish
Julieta
Problem  3

FInd the exact values of cos \(\displaystyle\frac{\pi}{6}\) and sin\(\displaystyle\frac{\pi}{6}\).

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Penelope
Penelope
Nathan
Nathan
Julieta cc espanol spanish
Julieta
Problem  4
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Penelope
Penelope
Nathan
Nathan
Julieta cc espanol spanish
Julieta
Problem  5
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Penelope
Penelope
Nathan
Nathan
Julieta cc espanol spanish
Julieta
Problem  6

Find the values of the trignometric functions of \(\frac{\pi}{3}\) to complete Table 4.

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Penelope
Penelope
Nathan
Nathan
Julieta cc espanol spanish
Julieta
Problem  7
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Penelope
Penelope
Nathan
Nathan
Julieta cc espanol spanish
Julieta
Problem  8
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Penelope
Penelope
Nathan
Nathan
Julieta cc espanol spanish
Julieta
Problem  9
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Penelope
Penelope
Nathan
Nathan
Julieta cc espanol spanish
Julieta
Problem  10
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Penelope
Penelope
Nathan
Nathan
Julieta cc espanol spanish
Julieta

3
Right Triangle Trigonometry

Problem  1

Use the triangle in Frigure 3 to find the six trigonometric functions of \(\theta\).

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Penelope
Penelope
Gordon cc
Gordon
Julieta cc espanol spanish
Julieta
Problem  2
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Choose instructor to watch:
Penelope
Penelope
Gordon cc
Gordon
Julieta cc espanol spanish
Julieta
Problem  3
Choose instructor to watch:
Saba cc
Saba
Gordon cc
Gordon
Julieta cc espanol spanish
Julieta
Problem  4
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Find the unknown angle measure and the unknown length of sides of the triangle in Figure 9.

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Penelope
Penelope
Gordon cc
Gordon
Julieta cc espanol spanish
Julieta
Problem  5
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Penelope
Penelope
Gordon cc
Gordon
Julieta cc espanol spanish
Julieta
Problem  6

A surveyor stands 100 feet from the base of a building. From that point, the angle of elevation to the top of the building is 78 \(^{\circ}\). See Figure 13. Find the height of the building. Round your answer to two decinal places.

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Penelope
Penelope
Gordon cc
Gordon
Julieta cc espanol spanish
Julieta
Problem  7
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A traffic helicopter hovering 500 feet above ground observes a police car on the ground at an angle of 25 \(^{\circ}\). See Figure 14. What is the distance of the helicopter from the police car, to the nearest foot?

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Penelope
Penelope
Gordon cc
Gordon
Julieta cc espanol spanish
Julieta
Problem  8

An observer meansures an angle of elevation of 41 \(^{\circ}\) to the top of a lighthouse from a certain point on the ground. She then walks 15 feet closer to the lighthouse and measures an angle of elevaion of 44\(^{\circ}\). See Figure 15. How tall is the lighthouse? Round your answer to two decimal places.

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Penelope
Penelope
Gordon cc
Gordon
Julieta cc espanol spanish
Julieta

4
Trigonometric Functions of Any Angle Using Right Triangles

Problem  1

In Figure 2 and Figure 3, find the exact values of all the trigonometric functions of each value of \(\theta\).

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Penelope
Penelope
Tim
Tim
Julieta cc espanol spanish
Julieta
Problem  2
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Choose instructor to watch:
Saba cc
Saba
Tim
Tim
Julieta cc espanol spanish
Julieta
Problem  3
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Find the exact values of all six trignometric functions of

a. \(\theta\) = 90\(^{\circ}\)

b. \(\theta\) = 180\(^{\circ}\)

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Penelope
Penelope
Tim
Tim
Julieta cc espanol spanish
Julieta
Problem  4
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Find the reference angle for each of the following angles.

a. \(\theta\) = 135\(^{\circ}\)

b. \(\theta\) = \(-110\) \(^{\circ}\)

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Penelope
Penelope
Tim
Tim
Julieta cc espanol spanish
Julieta
Problem  5
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Choose instructor to watch:
Penelope
Penelope
Tim
Tim
Julieta cc espanol spanish
Julieta
Problem  6

Find

a. sin 480\(^{\circ}\)

b. cos (\(-90\) \(^{\circ}\))

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Penelope
Penelope
Tim
Tim
Julieta cc espanol spanish
Julieta
Problem  7
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Saba cc
Saba
Tim
Tim
Julieta cc espanol spanish
Julieta
Problem  8
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Use a calculator to find the following. Round your answers to four decimal places.

a. sin 242\(^{\circ}\)

b. cot 318\(^{\circ}\)

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Penelope
Penelope
Tim
Tim
Julieta cc espanol spanish
Julieta

5
Graphs of the Sine and Cosine Functions

Problem  1
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Gordon cc
Gordon
Molly S. cc
Molly S.
Problem  2
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Gordon cc
Gordon
Stephanie
Stephanie
Problem  3
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Choose instructor to watch:
Gordon cc
Gordon
Saba cc
Saba
Ryan
Ryan
Julieta cc espanol spanish
Julieta
Problem  4
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Choose instructor to watch:
Gordon cc
Gordon
Saba cc
Saba
Ryan
Ryan
Julieta cc espanol spanish
Julieta
Problem  5
Choose instructor to watch:
Gordon cc
Gordon
Stephanie
Stephanie
Julieta espanol spanish
Julieta
Problem  6
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Choose instructor to watch:
Gordon cc
Gordon
Stephanie
Stephanie
Julieta espanol spanish
Julieta
Problem  7
Choose instructor to watch:
Gordon cc
Gordon
Stephanie
Stephanie
Julieta espanol spanish
Julieta
Problem  8
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Gordon cc
Gordon
Stephanie
Stephanie
Julieta espanol spanish
Julieta

6
Graphs of Other Trigonometric Functions

Problem  1
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Tim
Tim
Stephanie
Stephanie
Julieta espanol spanish
Julieta
Problem  2
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Sketch the graph of at least two full periods of the function cot3x.

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Tim
Tim
Stephanie
Stephanie
Julieta espanol spanish
Julieta
Problem  3
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Tim
Tim
Stephanie
Stephanie
Julieta espanol spanish
Julieta
Problem  4
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Choose instructor to watch:
Tim
Tim
Stephanie
Stephanie
Julieta espanol spanish
Julieta

7
Inverse Trigonometric Functions

Problem  1
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Breylor
Breylor
Shelby
Shelby
Nathan
Nathan
Julieta espanol spanish
Julieta
Problem  2
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Breylor
Breylor
Shelby
Shelby
Nathan
Nathan
Julieta espanol spanish
Julieta
Problem  3
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Shelby
Shelby
Breylor
Breylor
Julieta espanol spanish
Julieta
Problem  4
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Mr. Hampton
Mr. Hampton
Shelby
Shelby
Breylor
Breylor
Julieta espanol spanish
Julieta
Problem  5

A ramp is to be constructed with a slope of \(\displaystyle\frac{1}{10}\). See Figure 12. Find the acute angle that the ramp makes with the horizontal. Express the angle in degrees.

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Shelby
Shelby
Breylor
Breylor
Julieta espanol spanish
Julieta
Problem  6
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Shelby
Shelby
Breylor
Breylor
Julieta espanol spanish
Julieta
Problem  7
Choose instructor to watch:
Shelby
Shelby
Breylor
Breylor
Julieta espanol spanish
Julieta
Problem  8
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Choose instructor to watch:
Shelby
Shelby
Breylor
Breylor
Julieta espanol spanish
Julieta