Deck 5: Introduction to Trigonometric Functions

Question 1

Determine the measure of the complement of a 74° angle.

A) 16°
B) 106°
C) 196°
D) 286°

Answer 1

16°

Question 2

To convert degrees to radians, multiply by ______.

A)
B)
C)
D)

Answer 2

Question 3

A 3-foot pole casts a shadow of 4 feet. How tall is a tree with a shadow of 14 feet?

Answer 3

The tree is ft (or 10.5 ft) tall.

Question 4

If $\theta$ is not a special angle, multiply by ______ to convert radians to degrees.

A)
B)
C)
D)

Question 5

Convert 160° to radians in exact form, without the use of a calculator.

A). $\theta$ = rad
B). $\theta$ = rad
C). $\theta$ = rad
D). $\theta$ = 28,800 $\pi$ rad

Question 6

Determine the measure of the supplement of a 45° angle.

A) 45°
B) 135°
C) 225°
D) 315°

Question 7

Complementary angles sum to _____.

A) 45°
B) 90°
C) 180°
D) 360°

Question 8

Convert from DMS (degree/minute/sec) notation to decimal degrees. Round to hundredths of a degree. 59°34′18′′

A) 59.51°
B) 59.53°
C) 59.55°
D) 59.57°

Question 9

A 9 cm stick is leaning against the curb. If the base of the stick is 4.5 cm from the bottom of the curb, find the measure of the angle the stick makes with the ground, angle $\alpha$ and the height of the curb x.

Question 10

Find the measure of angle A.

Question 11

Convert from DMS (degree/minute/sec) notation to decimal degrees.
114°45′

Question 12

Use the formula for arc length to find the value of the unknown quantity: s = r $\theta$ .
$\theta$ = ; r = 93 km

A) s = 310 $\pi$ km
B) s = km
C) s = 155 $\pi$ km
D) s = km

Question 13

_______ angles measure greater than 90°.

Question 14

Find the measure of angle B.

A) 50°
B) 55°
C) 60°
D) 65°

Question 15

Use the formula for arc length to find the value of the unknown quantity: s = r $\theta$ .
$\theta$ = 2.1; r = 220 ft.

Question 16

Use the formula for arc length to find the unknown quantity: s = r $\theta$ . Round your answer to the nearest hundredth of an inch.
$\theta$ = 280°; s = 68 in.

Question 17

Convert from decimal degrees to DMS (degree/minute/sec) notation. Round to the nearest second.
8.3503°

Question 18

Use the formula for area of a circular sector to find the value of the unknown quantity: . Round your answer to the nearest tenth of a yard.
$\theta$ = ; A = 12.8 yd.

Question 19

Use the formula for area of a circular sector to find the value of the unknown quantity: . $\theta$ = 6; r = 15.4 m

A) A = 46.2 m²
B) A = 711.48 m²
C) A = 1422.96 m²
D) A = 277.2 m²

Question 20

Convert from decimal degrees to DMS (degree/minute/sec) notation. 100.05°

A) 100°1′
B) 100°3′
C) 100°5′
D) 100°7′

Question 21

State the exact value of sin $\pi$ . A diagram may help.

Question 22

Use the following to answer questions :
Find the reference angle associated with the rotation.

A)
B)
C)
D)

Question 23

Convert 5.2135 rad to degrees. Round to the nearest tenth.

A) 0.1°
B) 298.7°
C) 597.4°
D) 938.4°

Question 24

Convert rad to degrees.

Question 25

Use the following to answer questions :
The wheels on a vehicle have a radius of 29 inches and are turning at 250 revolutions per minute.
What is the linear velocity of the wheels in miles per hour?

A) about 64.8 mi/hr
B) about 65.2 mi/hr
C) about 65.6 mi/hr
D) about 66.9 mi/hr

Question 26

Given the point (x, -0.6) lies on the unit circle, complete the ordered pair for quadrant IV. Answer in radical form as needed.

A) (0.8, -0.6)
B) (-0.8, -0.6)
C) (0.4, -0.6)
D) (-0.4, -0.6)

Question 27

State the exact value of . A diagram may help.

A)
B)
C)
D)

Question 28

State the exact value of . A diagram may help.

A) -1
B) 0
C) 1
D) undefined

Question 29

Convert 6° to radians. Round to the nearest ten-thousandth.

Question 30

State the exact value of . A diagram may help.

A)
B)
C)
D)

Question 31

Verify that the point is on the unit circle, then use symmetry to find three more points on the circle.

Question 32

Use the following to answer questions :
Find the associated point (x, y).

A)
B)
C)
D)

Question 33

Use the following to answer questions :
The wheels on a vehicle have a radius of 29 inches and are turning at 250 revolutions per minute.

-What is the angular velocity of the wheels?

A) 1097 $\pi$ rad/min
B) 1100 $\pi$ rad/min
C) 1105 $\pi$ rad/min
D) 1111 $\pi$ rad/min

Question 34

Use the symmetry of the circle and reference arcs as needed to state the exact value of . A diagram may help.

A)
B)
C)
D)

Question 35

Use the following to answer questions :
The wheels on a vehicle have a radius of 29 inches and are turning at 250 revolutions per minute.
What is the linear velocity of the wheels in inches per minute?

A) about 84,820.6 in/min
B) about 84,821.8 in/min
C) about 84,823.0 in/min
D) about 84,824.8 in/min

Question 36

Use the symmetry of the circle and reference arcs as needed to state the exact value of . A diagram may help.

Question 37

State the exact value of cos 0. A diagram may help.

A) 1
B) 0
C) -1
D) undefined

Question 38

State the exact value of . A diagram may help.

A) -1
B) 0
C) 1
D) undefined

Question 39

State the exact value of . A diagram may help.

Question 40

Find the reference angle associated with the rotation.

Question 41

Use a reference rectangle and the rule of fourths to draw an accurate sketch through at least one complete cycle where t > 0. y =

A)

B)

C)

D)

Question 42

Without using a calculator, find two values of t (where possible) in [0, 2π) such that sec t is undefined.

Question 43

Use the symmetry of the circle and reference arcs as needed to state the exact value of cot $\pi$ . A diagram may help.

A) 1
B) 0
C) -1
D) undefined

Question 44

Use the symmetry of the circle and reference arcs as needed to state the exact value of . A diagram may help.

A) -1
B) 0
C) 1
D) undefined

Question 45

Use a reference rectangle and the rule of fourths to draw an accurate sketch through at least one complete cycle where t > 0.
y = -2 sin t

Question 46

Use steps I through IV given in Section 3 to draw a sketch of y = sin t for t $\in$ .

Question 47

Use a reference rectangle and the rule of fourths to draw an accurate sketch through at least one complete cycle where t > 0.
y = cos t

Question 48

Without using a calculator, find the value of t in [0, 2π) that corresponds to tan t = with t in QIV.

A)
B)
C)
D)

Question 49

Without using a calculator, find two values of t (where possible) in [0, 2π) that make cos t = true.

A)
B)
C)
D)

Question 50

Find an additional value of t (to four decimal places) in [0, 2?) that makes cos t $\approx$ -0.3379 true, given that cos 1.9155 $\approx$ -0.3379.

Question 51

Use the following to answer questions :
y = -8 sin

-State the period.

A)
B)
C) 5 $\pi$
D) 10 $\pi$

Question 52

Use the symmetry of the circle and reference arcs as needed to state the exact value of tan 0. A diagram may help.

A) 1
B) 0
C) -1
D) undefined

Question 53

Use the following to answer questions :
y = -8 sin
State the amplitude.

A) 4
B) -4
C) 3
D) -3

Question 54

Use a reference rectangle and the rule of fourths to draw an accurate sketch through at least one complete cycle where t > 0. y =

A)

B)

C)

D)

Question 55

Without using a calculator, find the value of t in [0, 2?) that corresponds to sin t = -1. t is a quadrantal angle.

A) 0
B)
C). $\pi$
D)

Question 56

Use the symmetry of the circle and reference arcs as needed to state the exact value of . A diagram may help.

A) -1
B) 0
C) 1
D) undefined

Question 57

Without using a calculator, find the value of t in [0, 2π) that corresponds to sin t = with t in QII.

Question 58

Use steps I through IV given in Section 3 to draw a sketch of y = cos t for t $\in$ [- $\pi$ , $\pi$ ].

A)

B)

C)

D)

Question 59

Use a reference rectangle and the rule of fourths to draw an accurate sketch through at least one complete cycle where t > 0.
y =

Question 60

Use steps I through IV given in Section 3 to draw a sketch of y = sin t for t $\in$ [- $\pi$ , $\pi$ ].

A)

B)

C)

D)

Question 61

State the value of t without the use of a calculator, given t $\in$ [0, 2?) terminates in QII. cot t =

A)
B)
C)
D)

Question 62

Use the following to answer questions :
y =
State the amplitude.

Question 63

State the value of without the use of a calculator.

A)
B)
C)
D)

Question 64

Graph f(t) = 3 tan t over the interval [-2π, 2π].

Question 65

Graph f(t) = cot(2t) over the interval [-π, π].

Question 66

Use the values for sin t and cos t to complete the table.

Question 67

The graph below is of the form y = A cos(Bt). Use the characteristics illustrated to determine its equation.

Question 68

State the value of t without the use of a calculator, given t $\in$ [0, 2?) terminates in QIII.
tan t = 1

Question 69

State the value of without the use of a calculator.

A) -1
B) 0
C) 1
D) undefined

Question 70

Use the following to answer questions :
y =
State the period.

Question 71

Draw the graph of y = 5 csc(2t) by applying observations made in this chapter about the related sine graph.

A)
B)
C)
D)

Question 72

Graph f(t) = -3 cot(πt) over the interval [-2, 2].

A)

B)

C)

D)

Question 73

The graph below is of the form y = A sin(Bt). Use the characteristics illustrated to determine its equation.

A)
B)
C)
D)

Question 74

Find the equation of the graph, given it is of the form y = A tan(Bt).

A)
B)
C)
D)

Question 75

Use the given solution and the period of the function to name all real roots. t = , tan t ≈ 0.2936

A)
B)
C)
D)

Question 76

Use the following to answer questions :
The data in the table can be modeled using the function y = A tan(Bx).

State the period of the function.

A) 4
B) 8
C) 16
D) 32

Question 77

Use the following to answer questions :
y =
Use a reference rectangle and the rule of fourths to draw an accurate sketch through at least one complete cycle where t > 0.

Question 78

Draw the graph of y = 3 sec t by applying observations made in this chapter about the related cosine graph.

Question 79

Use the values for sin t and cos t to complete the table.

Question 80

Given t ≈ 5.9 is a solution to cot t = -2.48, use the period of the function to name three additional solutions.

A) 4.3, 7.5, 9.0
B) 2.8, 9.0, 12.2
C) 1.2, 10.6, 15.3
D) 6.7, 7.5, 8.3