Deck 6: Trigonometric Algebra and Geometry

Question 1

Suppose the figure below is part of the graph of the function 8sin(9x). What is the value of b?

A) 9.
B) 16
C) 8
D) 9

Answer 1

8

Question 2

Find the smallest positive number c such that the figure below is part of the graph of the function sin(x + 5c). Give the exact answer.

Answer 2

Question 3

Sketch the graphs of the functions -5sin(x) and sin(-5x) on the interval [- $\pi$ , $\pi$ ].

Answer 3

Question 4

What is the range of the function 3sin(6x)?

Question 5

What is the amplitude of the function 9sin(8x)?

Question 6

What is the period of the function 6sin(19x)?

A)

B)

C)

D) 2 $\pi$

Question 7

What is the range of the function 4 + cos(4 - x)?

Question 8

What is the amplitude of the function 3 + cos(1 - x)?

Question 9

What is the period of the function 3 + cos(5 - x)?

Question 10

What is the range of the function ?

Question 11

What is the amplitude of the function
?

Question 12

What is the period of the function ?

A)

B)

C) 3
D) 6

Question 13

By what fraction of the period of
has the graph been shifted left to obtain the graph of ?

Question 14

Find two distinct values for a so that acos(bx + c) + d, has amplitude 5.

Question 15

Find values for a and d, respectively, with a > 0, so that f(x) = acos(bx + c) + d has range [8, 14].

A) 4, 11
B) 3, 11
C) 4, 10
D) 3, 10

Question 16

Find values for a, d, c, and b, respectively, with a > 0, b > 0, and , so that f(x) = acos(bx + c) + d has range [9, 17], f(0) = 15, and f has period 18. Give the exact answer.

Question 17

What is the range of the function 7sin²(4x)?

Question 18

What is the amplitude of the function 18cos²(9x)?

A) 18
B) 9
C) 81
D) 324

Question 19

What is the period of the function 5sin²(3x)? Give the exact answer.

Question 20

Sketch the graph of the function cos²(4x) on the interval [- $\pi$ , $\pi$ ].

Question 21

For and , evaluate each of the following. Round your answers to the nearest hundredth.

A) cos(x + y)
B) cos x + cos y

Question 22

For x = 5.6 radians and y = 2.6 radians, evaluate each of the following. Round your answers to the nearest hundredth.

A) sin(x - y)
B) sin x - sin y

Question 23

Find an exact expression for . The following information will be useful.

Question 24

Find an exact expression for . The following information will be useful:

A)
B)
C)

D)

Question 25

Find an exact expression for
. The following information will be useful:

Question 26

Find an exact expression for . The following information will be useful:

A)

B)

C)

D)

Question 27

Evaluate cos(x + y) assuming that
. Assume also that x is in the interval and y is in the interval . Give the exact answer.

Question 28

Evaluate sin(u + v) assuming that
. Assume also that u is in the interval
and that v is in the interval . Give the exact answer.

Question 29

Evaluate cos(x - y) assuming that
. Assume also that x is in the interval
and that y is in the interval . Give the exact answer.

Question 30

Evaluate sin(u - v) assuming that
. Assume also that u is in the interval and that v is in the interval . Give the exact answer.

Question 31

Evaluate tan(x + y) assuming that
. Assume also that x is in the interval
and that y is in the interval . Give the exact answer.

Question 32

Evaluate tan(u - v) assuming that

. Assume also that u is in the interval
and that v is in the interval . Give the exact answer.

Question 33

Evaluate .

A)

B)

C)
D)

Question 34

Evaluate
. Give the exact answer.

Question 35

Find a formula for
.

Question 36

Find a formula for:

A)
B)
C)
D)

Question 37

Find a formula for
.

Question 38

Find a formula for:

Question 39

Find a formula for
.

Question 40

Find a formula for

A)

B)

C)

D)

Question 41

For , evaluate each of the following; round your answers to the nearest hundredth.

A) cos 2 $\theta$
B) 2cos $\theta$

Question 42

For $\theta$ = -5 radians, evaluate each of the following; round your answers to the nearest hundredth.

A) sin 2 $\theta$
B) 2sin $\theta$

Question 43

For , evaluate each of the following; round your answers to the nearest hundredth.

A)

B)

Question 44

Given that , find an exact expression for
.

Question 45

Evaluate tan u assuming that u is in the interval
And .

A)

B)

C)

D)

Question 46

Evaluate sin 2u assuming that u is in the interval
and . Give the exact answer.

Question 47

Evaluate assuming that v is in the interval
and . Give the exact answer.

Question 48

Evaluate Assuming that u is in the interval
And
.

A)

B)

C)

D)

Question 49

Evaluate cos u assuming that u is in the interval
And
.

A)

B)

C)

D)

Question 50

Evaluate tan u assuming that u is in the interval
and
. Give the exact answer.

Question 51

Evaluate tan 2u assuming that u is in the interval

and . Give the exact answer.

Question 52

Evaluate assuming that u is in the interval and . Give the exact answer.

Question 53

Evaluate assuming that u is in the interval and . Give the exact answer.

Question 54

Evaluate cos u assuming that u is in the interval And
.

A)

B)

C)

D)

Question 55

Evaluate sin 2u assuming that u is in the interval
and . Give the exact answer.

Question 56

Evaluate assuming that u is in the interval and . Give the exact answer.

Question 57

Evaluate Assuming that u is in the interval And
.

A)

B)

C)

D)

Question 58

Find an exact expression for

.

Question 59

Find an exact expression for
.

Question 60

Find an exact expression for
.

Question 61

-Given a = 5, B = , C = . Evaluate:

A) A
B) b
C) c
Round b and c to the nearest tenth.

Question 62

-Given a = 12, B = , C = . Evaluate b. Round b to the nearest tenth.

A) 23.6
B) 26.4
C) 24.6
D) 22.6

Question 63

-Given a = 10, , . Evaluate:

A) A
B) b
C) c
Round b and c to the nearest tenth.

Question 64

-Given a = 3, b = 5, c = 6. Evaluate:

A) A
B) B
C) C
Round your answers to the nearest tenth.

Question 65

-Given a = 8, b = 7, c = 5. Evaluate:

A) A
B) B
C) C
Round your answers to the nearest tenth.

Question 66

-Given a = 7, b = 5, c = 8. Evaluate:

A) A
B) B
C) C
Round your answers to the nearest tenth.

Question 67

-Given a = 14, , . Evaluate: B, b, c
Round your answers for b and c to the nearest tenth.

A) B: B: 14.0C: 31.5
B) B: ,B: 25.2C: 31.5
C) B: b: 25.2C: 31.5
D) B: b: 14.0C: 31.5

Question 68

-Given a = 3, b = 4, c = 5. Evaluate:

A) A
B) B
C) C
Round your answers to the nearest tenth.

Question 69

-Given a = 3, b = 4, C =

. Evaluate:

A) c
B) A
C) B
Round your answers to the nearest tenth.

Question 70

-Given a = 6, b = 7, C = 2 radians. Evaluate:

A) c
B) A
C) B
Angles should be given in radians rounded to the nearest hundredth.

Question 71

-Given a = 4, b = 3, C = 1. Evaluate:

A) c
B) A
C) B
Angles should be given in radians rounded to the nearest hundredth.

Question 72

-Given a = 7, b = 6, B =
. Evaluate:

A) A where A <
B) C
C) c
Round your answers to the nearest tenth.

Question 73

-Given a = 4, b = 3, C =
. Evaluate A.

A)

B)

C)

D)

Question 74

-Given a = 9, b = 11, B = . Evaluate:

A) A where A <

B) C
C) c
Round your answers to the nearest tenth.

Question 75

-Given a = 4, b = 3, B = . Evaluate:

A) A where A >

B) C
C) c
Round your answers to the nearest tenth.

Question 76

-Given a = 9, b = 7, B = . Evaluate:

A) A where A >

B) C
C) c
Round your answers to the nearest tenth.

Question 77

-Given a = 5, c = 8, B = . Evaluate b.

A) 3.2
B) 4.7
C) 2.7
D) 3.7

Question 78

-Given a = 11, c = 8, B = . Evaluate:

A) b
B) A
C) C
Round your answers to the nearest hundredth.

Question 79

-Given a = 11, c = 13, B = . Evaluate:

A) b
B) A
C) C
Round your answers to the nearest hundredth.

Question 80

-Given a = 12, c = 10, B = . Evaluate C.

A)

B)

C)

D)