Download MULTIPLE CHOICE. Choose the one alternative that best completes

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MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
Use the fundamental identities to simplify the expression.
1) cos - cos sin2
A) tan2
B) sin
C) cos3
Use a sum or difference identity to find the exact value.
2) sin 15° cos 105° + cos 15° sin 105°
3
3
A)
B) 2
2
D) sec2
2)
C)
1
4
D) -
1
2
Use the fundamental identities to find the value of the trigonometric function.
8
3) Find sin if sec = - and tan < 0.
5
A) -
39
8
B)
39
8
C) -
Use the fundamental identities to simplify the expression.
4) 1 - sin2
A) cot2
B) - cos2
5
8
3)
D)
39
64
4)
C) cos2
D) cos
Use identities to find the indicated value for each angle measure.
5
Find sin(2 ).
5) cos = , sin < 0
13
A)
119
169
B) -
119
169
5)
C) -
120
169
D)
120
169
Use the fundamental identities to simplify the expression.
sec2 x
- tan x
6)
tan x
A) tan2 x
6)
B) csc x
C) cot x
D) tan x
Perform the transformation.
7) Write sec x in terms of sin x.
7)
A) ± 1 - sin 2 x
B)
1 - sin2 x
1 - sin2 x
D)
C)
±
1)
1
± sin x
1 - sin2 x
1 - sin2 x
±
1 - sin2 x
sin x
Use a sum or difference identity to find the exact value.
8) sin 10° cos 50° + cos 10° sin 50°
1
1
A)
B)
2
6
9)
8)
C)
3
2
D)
3
3
tan 20° + tan 10°
1 - tan 20° tan 10°
A)
9)
1
2
B)
3
3
C) 2
Use the fundamental identities to find the value of the trigonometric function.
10) Find sin if cot = - 6 and cos < 0.
37
1
A) - 37
B) C)
37
6
11) Find cos
A) -
5
12
if sin
=-
5
and
13
B)
D)
3
D)
37
6
10)
11)
is in quadrant III.
12
5
C) -
13
5
Perform the indicated operations and simplify the result so there are no quotients.
12) tan2 - 3 sin tan sec
A) 1 + cot
B) sin tan
C) sec csc
Decide whether the expression is or is not an identity.
13) sin2 x + cos2x = 1
A) Identity
D) -
12
13
D) -2 tan2
13)
B) Not an identity
Complete the sentence so the result is an identity. Let x be any real number.
14) sin x = ( )(cos x)
A) cot x
B) sec x
C) tan x
12)
D) csc x
14)
Write the expression in terms of sine and cosine, and simplify so that no quotients appear in the final expression.
15) tan2 csc2
15)
2
2
3
A) sin
B) tan
C) sec
D) cos
Use the fundamental identities to find the value of the trigonometric function.
11
and is in quadrant III.
16) Find sin if cos = 6
A) -
25
36
B)
5
6
C) -
2
5
6
16)
D) -
3
12
Find the exact value of the expression using the provided information.
1
1
17) Find sin(s - t) given that cos s = , with s in quadrant I, and sin t = , with t in quadrant II.
3
4
A)
-12 2 - 1
30
B)
-12 30 - 1
2
C)
-30 2 - 1
12
D)
-2 30 - 1
12
Use the fundamental identities to simplify the expression.
1
+ sec cos
18)
cot2
A) tan2
18)
B) csc2
D) sec2
C) 1
Use identities to fill in the blank with the appropriate trigonometric function name.
1
19) sec 30° =
60°
A) csc
B) cos
C) sin
19)
D) sec
Using a sum or difference identity, write the following as an expression involving functions of x.
20) sin (x + 45°)
A) -cos x
C)
D)
2
2
cos x sin x
2
2
Tell whether the statement is true or false.
17
= cos cos - sin sin
21) cos
72
9
8
9
8
21)
A) True
B) False
Use an identity to write the expression as a single trigonometric function or as a single number.
1 + cos 84°
22)
1 - cos 84°
B) cot 42°
Use a sum or difference identity to find the exact value.
23) tan(- 15°)
3+4
A) - 3 + 2
B)
2
C) sin 42°
D) tan 42°
3-2
3-4
2
22)
23)
C)
D)
Use an identity to write the expression as a single trigonometric function or as a single number.
24) sin 22.5° cos 22.5°
2
3
2
A)
B)
C) 3
D)
4
3
2
25) 2 cos2 75° - 1
3
A) 2
20)
B) sin x
2
2
cos x +
sin x
2
2
A) cos 42°
17)
24)
25)
1
B) 2
1
C)
2
3
3
D)
2
26) cos2 4x - sin2 4x
1
A) sin 16x
2
26)
B) cos 4x
C) cos 8x
Write the product as a sum or difference of trigonometric functions.
27) cos 35° sin 21°
1
1
A) (cos 56° - cos 14°)
B) (sin 56° + sin 14°)
2
2
C)
1
(cos 56° + cos 14°)
2
D)
B) -2 sin 32° sin(-12°)
D) -2 cos 32° sin(-12°)
Write the product as a sum or difference of trigonometric functions.
30) 2 sin 5x sin 13x
A) cos 8x - cos 18x
C)
B) cos 18x + cos 8x
1
(cos 18x + cos 8x)
2
D) sin 18x + sin 8x
4
27)
1
(sin 56° - sin 14°)
2
Rewrite the following as a product of trigonometric functions.
28) sin 19° + sin 35°
A) 2 sin 27° sin(-8°)
B) 2 cos 27° sin(-8°)
C) 2 sin 27° cos(-8°)
D) 2 cos 27° cos(-8°)
29) cos 20° - cos 44°
A) -2 cos 32° cos(-12°)
C) -2 sin 32° cos(-12°)
D) 2 sin 4x
28)
29)
30)