Deck 6: Trigonometric Identities and Conditional Equations

Question 1

Write the expression in terms of sines and/or cosines, and then simplify.
tan xsec x + 1 (sin x - 1)

A)
B)
C)
D)

Answer 1

Question 2

Write the expression in terms of sines and/or cosines, and then simplify.

A)
B)
C)
D)

Answer 2

Question 3

Write the expression in terms of sines and/or cosines, and then simplify.

A)
B)
C) cos x - sin x
D)

Answer 3

Question 4

Write the expression in terms of sines and/or cosines, and then simplify.

A) cos x
B) sec x
C) csc x
D) sin x

Question 5

Express the given trigonometric function in terms of the indicated function.
sin in terms of csc

A)
B)
C)
D)

Question 6

Write the expression in terms of sines and/or cosines, and then simplify.

A)
B)
C)
D)

Question 7

Write the expression in terms of sines and/or cosines, and then simplify.
tan cot

A) 1
B)
C)
D)

Question 8

Write the expression in terms of sines and/or cosines, and then simplify.

A) 1
B)
C)
D)

Question 9

Write the expression in terms of sines and/or cosines, and then simplify.

A)
B)
C)
D)

Question 10

Write the expression in terms of sines and/or cosines, and then simplify.

A) sin x + csc x
B) csc x
C) sec x + sin x
D) cos x

Question 11

Write the expression in terms of sines and/or cosines, and then simplify.

A) sin x
B) csc x
C) cos x
D) sec x

Question 12

Write the expression in terms of sines and/or cosines, and then simplify.
cos x + tan x sin x

A) csc x
B) sec x
C)
D) sin x + cos x

Question 13

Write the expression in terms of sines and/or cosines, and then simplify.
tan x csc x

A) csc x
B) sec x
C) 1
D) cos x

Question 14

Write the expression in terms of sines and/or cosines, and then simplify.

A)
B) sin x
C)
D)

Question 15

Write the expression in terms of sines and/or cosines, and then simplify.
cot x sin x - tan x cos x

A)
B)
C)
D) cos x - sin x

Question 16

Write the expression in terms of sines and/or cosines, and then simplify.

A) 1
B)
C)
D)

Question 17

Write the expression in terms of sines and/or cosines, and then simplify.
(tan x csc x + 1)(sec x - 1)

A) tan x + sec x - sin x - 1
B) sec x - cos x
C)
D)

Question 18

Write the expression in terms of sines and/or cosines, and then simplify.
sec x + csc x

A)
B)
C) cos x - sin x
D)

Question 19

Write the expression in terms of sines and/or cosines, and then simplify.

A)
B)
C) cos x - sin x
D)

Question 20

Write the expression in terms of sines and/or cosines, and then simplify.
cot x sec x

A) sin x
B) sec x
C) csc x
D) cos x

Question 21

Use identities to find the exact value of the trigonometric function.
Find sin if cot

A)
B)
C)
D) -17

Question 22

Use identities to find the exact value of the trigonometric function.
Find cos , given that sin and is in quadrant II.

A)
B)
C)
D)

Question 23

Use identities to find the exact value of the trigonometric function.
Find sin if tan

A)
B)
C)
D)

Question 24

Express the given trigonometric function in terms of the indicated function.
sec in terms of cot

A)
B)
C)
D)

Question 25

Use identities to find the exact value of the trigonometric function.
Find csc if cot

A)
B) - 4
C) 4
D)

Question 26

Use identities to find the exact value of the trigonometric function.
Find sin given that cos

A)
B)
C)
D)

Question 27

Use identities to find the exact value of the trigonometric function.
Find cot if tan and is in quadrant III.

A)
B)
C)
D)

Question 28

Use identities to find the exact value of the trigonometric function.
Find sec if cos

A) -6
B)
C) 6
D)

Question 29

Use identities to find the exact value of the trigonometric function.
Find tan if sec

A) 5
B)
C)
D) -5

Question 30

Use identities to find the exact value of the trigonometric function.
Find cos if sin .

A)
B)
C)
D)

Question 31

Express the given trigonometric function in terms of the indicated function.
csc in terms of tan

A)
B)
C)
D)

Question 32

Express the given trigonometric function in terms of the indicated function.
cos in terms of cot

A)
B)
C)
D)

Question 33

Express the given trigonometric function in terms of the indicated function.
tan in terms of sin

A)
B)
C)
D)

Question 34

Use identities to find the exact value of the trigonometric function.
Find cot if csc

A) 5
B)
C)
D)

Question 35

Use identities to find the exact value of the trigonometric function.
Find cos if tan .

A)
B) -37
C)
D)

Question 36

Use identities to find the exact value of the trigonometric function.
Find cot if sec and is in quadrant IV.

A)
B) 2
C)
D) -2

Question 37

Use identities to find the exact value of the trigonometric function.
Find tan if cos

A)
B)
C) 4
D)

Question 38

Use identities to find the exact value of the trigonometric function.
Find cos given that csc is in quadrant IV.

A)
B)
C)
D)

Question 39

Express the given trigonometric function in terms of the indicated function.
cot in terms of tan

A)
B)
C)
D)

Question 40

Use identities to find the exact value of the trigonometric function.
Find sin given that cos

A)
B)
C)
D)

Question 41

Use odd and even identities to simplify the expression.
(1 + sec x)(1 - sec(-x))

A)
B)
C)
D)

Question 42

Use odd and even identities to simplify the expression.

A) -1
B) 1
C)
D)

Question 43

Use odd and even identities to simplify the expression.

A) -csc x
B) -sec x
C) sec x
D) csc x

Question 44

Find an equivalent algebraic expression for the given composition.
sec(arccos(x))

A)
B)
C)
D)

Question 45

Use identities to find the exact value of the trigonometric function.
Find tan given that sin

A)
B)
C)
D)

Question 46

Determine whether the function is odd, even, or neither.
f(x) =

A) Even
B) Neither
C) Odd

Question 47

Use odd and even identities to simplify the expression.

A) 0
B) -2 csc x
C) -2 sin x
D) 2 csc x

Question 48

Use odd and even identities to simplify the expression.
tan (-x) + tan x

A) - tan x
B) - 2 tan x
C) 2 tan x
D) 0

Question 49

Use identities to find the exact value of the trigonometric function.
Find sec given that tan

A)
B)
C)
D)

Question 50

Determine whether the function is odd, even, or neither.
f(t) = tan t + cos t

A) Even
B) Odd
C) Neither

Question 51

Use identities to find the exact value of the trigonometric function.
Find sin given that sec

A)
B)
C)
D)

Question 52

Find an equivalent algebraic expression for the given composition.
cot(arccos(x))

A)
B)
C)
D)

Question 53

Use odd and even identities to simplify the expression.
(1 + csc x)(1 + csc(-x))

A)
B)
C)
D)

Question 54

Use odd and even identities to simplify the expression.
cos (-x) sec (-x)

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

Question 55

Determine whether the function is odd, even, or neither.
f(x) = x + cos x

A) Odd
B) Even
C) Neither

Question 56

Use odd and even identities to simplify the expression.
csc x - csc (-x)

A) 2 csc x
B) 0
C) -2 csc x
D) - csc x

Question 57

Use odd and even identities to simplify the expression.
cos (-x) tan (-x)

A) sin x
B) - csc x
C) cos x
D) - sin x

Question 58

Determine whether the function is odd, even, or neither.
f(t) = t + cos t

A) Even
B) Neither
C) Odd

Question 59

Use odd and even identities to simplify the expression.
cos (-x) cos x - sin (-x) sin x

A) 2
B)
C) 1
D)

Question 60

Use identities to find the exact value of the trigonometric function.
Find sec given that sin is in quadrant II.

A)
B)
C)
D)

Question 61

Show that the equation is not an identity by listing the value(s) of the variable from among for which
the equation is false.

A)
B)
C)
D)

Question 62

Determine whether the function is odd, even, or neither.
f(x) = x + csc x

A) Even
B) Odd
C) Neither

Question 63

Determine whether the function is odd, even, or neither.
f( ) = 1 +

A) Odd
B) Neither
C) Even

Question 64

Choose the equivalent expression for the given expression.

A)
B)
C)
D)

Question 65

Show that the equation is not an identity by listing the value(s) of the variable from among for which
the equation is false.

A)
B)
C)
D)

Question 66

Choose the equivalent expression for the given expression.
sin(-x)

A) -sin x
B) cos x
C) -cos x
D) sin x

Question 67

Choose the equivalent expression for the given expression.

A)
B)
C)
D)

Question 68

Determine whether the function is odd, even, or neither.
f(x) = x + sec x

A) Even
B) Neither
C) Odd

Question 69

Choose the equivalent expression for the given expression.

A)
B)
C)
D)

Question 70

Choose the equivalent expression for the given expression.

A)
B)
C)
D)

Question 71

Show that the equation is not an identity by listing the value(s) of the variable from among for which
the equation is false.
sin + cos = tan

A) 0
B)
C)
D)

Question 72

Determine whether the function is odd, even, or neither.
f(x) = x csc x

A) Odd
B) Even
C) Neither

Question 73

Show that the equation is not an identity by listing the value(s) of the variable from among for which
the equation is false.

A)
B)
C)
D)

Question 74

Show that the equation is not an identity by listing the value(s) of the variable from among for which
the equation is false.

A)
B)
C)
D)

Question 75

Choose the equivalent expression for the given expression.

A)
B)
C)
D)

Question 76

Show that the equation is not an identity by listing the value(s) of the variable from among for which
the equation is false.

A)
B)
C)
D)

Question 77

Choose the equivalent expression for the given expression.

A)
B)
C)
D)

Question 78

Show that the equation is not an identity by listing the value(s) of the variable from among for which
the equation is false.

A)
B)
C)
D)

Question 79

Show that the equation is not an identity by listing the value(s) of the variable from among for which
the equation is false.
tan(-y) = tan y

A)
B)
C)
D)

Question 80

Show that the equation is not an identity by listing the value(s) of the variable from among for which
the equation is false.

A)
B)
C)
D)