Download Practice with Identities with key

More Practice with Identities
_______ 1.
The expression 2 sin 30° cos 30° has the same value as
A. sin 15°
B. cos 60°
C. sin 60°
D. cos 15°
_______ 2.
The expression 1 − 2 sin2 45° has the same value as
A. cos 90°
B. cos 45°
C. sin 90°
D. sin 22.5°
_______ 3.
If 𝑥 is an acute angle and cos 𝑥 = 5, then cos 2𝑥 is equal to
4
A.
6
25
B. −
_______ 4.
C.
2
25
D.
7
25
1
25
2
3
If sin 𝐴 = where 0° < 𝐴 < 90°, what is the value of sin 2𝐴?
A.
2√5
3
B.
2√5
9
C.
4√5
9
D. −
4√5
9
_______ 5.
The expression 10 sin 𝑡 cos 𝑡 is equivalent to
A. sin 5𝑡
B. 5 sin 2𝑡
C. cos 5𝑡
D. 5 cos 2𝑡
_______ 6.
The expression 4 − 8 sin2 𝑥 is equivalent to
A. 4 sin 2𝑥
B. sin 4𝑥
C. 4 cos 2𝑥
D. cos 4𝑥
_______ 7.
If
3𝜋
2
A.
B.
C.
D.
𝜃
< 𝜃 < 2𝜋 then the terminal side of 2 lies in
Quadrant I
Quadrant II
Quadrant III
Quadrant IV
_______ 8.
The expression cos 2 40° − sin2 40° has the same value as
A. sin 20°
B. sin 80°
C. cos 20°
D. cos 80°
_______ 9.
The expression
A.
B.
C.
D.
_______ 10.
is equivalent to
12 tan 𝜃
The expression 1−tan2 𝜃 is equivalent to
A.
B.
C.
D.
_______ 11.
tan 𝑡
cot 𝑡
sin 𝑡
2 tan 𝑡
sin 2𝑡
2 cos2 𝑡
tan 12𝜃
6 tan 𝜃
tan 6𝜃
6 tan 2𝜃
If 𝑥 is an acute angle and sin 𝑥 =
A.
25
169
B.
119
169
12
,
13
then cos 2𝑥 equals
25
C. − 169
119
D. − 169
_______ 12.
1−cos 30°
is
2
The expression √
A.
B.
C.
D.
_______ 13.
_______ 14.
tan 𝑣
cot 𝑣
− sin 𝑣
− cos 𝑣
1+cos 2𝑣
sin 2𝑣
is equivalent to
sin 30°
The expression 1+cos 30° is equivalent to
A.
B.
C.
D.
_______ 15.
sin 15°
sin 60°
cos 15°
cos 60°
The expression
A.
B.
C.
D.
equivalent to
cot 15°
tan 15°
tan 60°
cot 60°
The expression cos 4 𝑢 − sin4 𝑢 is equivalent to
A. cos 2𝑢
B. 1
C. cos 4𝑢
D. −1
_______ 16.
The expression sin 45° cos 30° + cos 45° sin 30° is equivalent to
A. cos 15°
B. cos 75°
C. sin 15°
D. sin 75°
_______ 17.
If 𝜃 is a positive angle and sin 2𝜃 =
√3
,
2
then (sin 𝜃 + cos 𝜃)2 equals
A. 1
B. 1 +
√3
2
C. 30°
D. 60°
_______ 18.
The expression
A.
B.
C.
D.
_______ 19.
sin 2𝑥
is
sin(−𝑥)
equivalent to
−2 sin 𝑥
2 sin 𝑥
−2 cos 𝑥
2 cos 𝑥
sin 𝑥
The expression 1+cos 𝑥 is equivalent to
A.
1+cos 𝑥
sin 𝑥
B. √
1+cos 𝑥
1−cos 𝑥
1−cos 𝑥
C. √1+cos 𝑥
D.
_______ 20.
_______ 21.
sin 𝑥
1−cos 𝑥
7
𝜋
𝑢
If cos 𝑢 = 25 and 0 < 𝑢 < 2 , then cos 2 equals
A.
4
5
B.
3
5
C.
7
5
D.
16
25
The expression sec 𝛼 sin 2𝛼 is equivalent to
A.
1
2
B. 2
C. 2 sin 𝛼
D. 2 cos 𝛼
_______ 22.
The expression 2 sin2 𝐴 + cos 2𝐴 is equivalent to
A. 1
B. 2
C. sin2 𝐴
D. − sin2 𝐴
_______ 23.
The expression
A.
B.
C.
D.
_______ 24.
The expression
A.
B.
C.
D.
_______ 25.
tan 60°
tan 15°
sin 60°
sin 15°
csc 𝑥
sec 𝑥
cot 𝑥
sin 𝑥
1−cos 30°
is
sin 30°
2 cos 𝑥
sin 2𝑥
equivalent to
is equivalent to
If sin 𝜃 = 𝑘, then the value of the expression sin 𝜃 cos 𝜃 tan 𝜃 is equivalent to
A. 1
B.
1
𝑘
C. 𝑘
D. 𝑘 2
More Practice with Identities KEY
C
_______ 1.
The expression 2 sin 30° cos 30° has the same value as
E. sin 15°
F. cos 60°
sine of double angle
G. sin 60°
H. cos 15°
A
_______ 2.
The expression 1 − 2 sin2 45° has the same value as
E. cos 90°
cosine of double angle
F. cos 45°
G. sin 90°
H. sin 22.5°
D
_______ 3.
If 𝑥 is an acute angle and cos 𝑥 = 5, then cos 2𝑥 is equal to
4
6
25
E.
F. −
C
_______ 4.
G.
2
25
H.
7
25
1
25
2 cos 2 𝑥 − 1 = 2 (
16
32 25
)−1=
−
25
25 25
2
3
If sin 𝐴 = where 0° < 𝐴 < 90°, what is the value of sin 2𝐴?
E.
2√5
3
F.
2√5
9
G.
4√5
9
H. −
2 √5
2 sin 𝐴 cos 𝐴 = 2 ( ) ( )
3
3
4√5
9
B
_______ 5.
The expression 10 sin 𝑡 cos 𝑡 is equivalent to
E. sin 5𝑡
F. 5 sin 2𝑡
G. cos 5𝑡
5(2 sin 𝑡 cos 𝑡)
H. 5 cos 2𝑡
C
_______
6.
The expression 4 − 8 sin2 𝑥 is equivalent to
E. 4 sin 2𝑥
F. sin 4𝑥
4(1 − 2 sin2 𝑥)
G. 4 cos 2𝑥
H. cos 4𝑥
B
_______
7.
If
3𝜋
2
E.
F.
G.
H.
𝜃
< 𝜃 < 2𝜋 then the terminal side of 2 lies in
Quadrant I
Quadrant II
Quadrant III
Quadrant IV
3𝜋 𝜃
< <𝜋
4
2
3
√5
2
D
_______ 8.
A
_______ 9.
The expression cos 2 40° − sin2 40° has the same value as
E. sin 20°
cosine of double angle
F. sin 80°
G. cos 20°
H. cos 80°
The expression
E.
F.
G.
H.
D
_______ 10.
is equivalent to
2 sin 𝑡 cos 𝑡
2 cos 2 𝑡
12 tan 𝜃
The expression 1−tan2 𝜃 is equivalent to
E.
F.
G.
H.
D
_______ 11.
tan 𝑡
cot 𝑡
sin 𝑡
2 tan 𝑡
sin 2𝑡
2 cos2 𝑡
tan 12𝜃
6 tan 𝜃
tan 6𝜃
6 tan 2𝜃
6(
2 tan 𝜃
)
1 − tan2 𝜃
If 𝑥 is an acute angle and sin 𝑥 =
E.
25
169
F.
119
169
12
,
13
then cos 2𝑥 equals
12 2 169 288
1 − 2 sin2 𝑥 = 1 − 2 ( ) =
−
13
169 169
25
119
H. − 169
1−cos 30°
is
2
The expression √
E.
F.
G.
H.
B
_______ 13.
E.
F.
G.
H.
B
_______ 14.
tan 𝑣
cot 𝑣
− sin 𝑣
− cos 𝑣
equivalent to
sine of half angle
1+cos 2𝑣
sin 2𝑣
is equivalent to
tangent of half angle upside-down
sin 30°
The expression 1+cos 30° is equivalent to
E.
F.
G.
H.
A
_______
15.
sin 15°
sin 60°
cos 15°
cos 60°
The expression
cot 15°
tan 15°
tan 60°
cot 60°
12
5
G. − 169
A
_______ 12.
13
tangent of half angle
The expression cos 4 𝑢 − sin4 𝑢 is equivalent to
E. cos 2𝑢
F. 1
(cos2 𝑢 − sin2 𝑢)(cos 2 𝑢 + sin2 𝑢) = (cos 2𝑢)(1)
G. cos 4𝑢
H. −1
D
_______
16.
The expression sin 45° cos 30° + cos 45° sin 30° is equivalent to
E. cos 15°
F. cos 75°
sin(45° + 30°)
G. sin 15°
H. sin 75°
B
_______ 17.
If 𝜃 is a positive angle and sin 2𝜃 =
√3
,
2
then (sin 𝜃 + cos 𝜃)2 equals
E. 1
F. 1 +
√3
2
sin2 𝜃 + 2 sin 𝜃 cos 𝜃 + cos2 𝜃 =
G. 30°
H. 60°
C
_______ 18.
The expression
E.
F.
G.
H.
C
_______ 19.
1 + 2 sin 𝜃 cos 𝜃 = 1 + sin 2𝜃
sin 2𝑥
is
sin(−𝑥)
equivalent to
−2 sin 𝑥
2 sin 𝑥
−2 cos 𝑥
2 cos 𝑥
2sin 𝑥 cos 𝑥
− sin 𝑥
sin 𝑥
The expression 1+cos 𝑥 is equivalent to
E.
1+cos 𝑥
sin 𝑥
F. √
1+cos 𝑥
1−cos 𝑥
tangent of half angle
1−cos 𝑥
G. √1+cos 𝑥
H.
A
_______ 20.
C
_______
21.
sin 𝑥
1−cos 𝑥
7
E.
4
5
F.
3
5
G.
7
5
H.
16
25
𝑢
7
1 + cos 𝑢 √1 + 25
16 4
√
=
=√ =
2
2
25 5
The expression sec 𝛼 sin 2𝛼 is equivalent to
E.
1
2
F. 2
G. 2 sin 𝛼
H. 2 cos 𝛼
A
_______
22.
𝜋
If cos 𝑢 = 25 and 0 < 𝑢 < 2 , then cos 2 equals
1
2 sin 𝛼 cos 𝛼
∙
cos 𝛼
1
The expression 2 sin2 𝐴 + cos 2𝐴 is equivalent to
E. 1
F. 2
2 sin2 𝐴 + 1 − 2 sin2 𝐴
2
G. sin 𝐴
H. − sin2 𝐴
B
_______ 23.
The expression
E.
F.
G.
H.
A
_______ 24.
The expression
E.
F.
G.
H.
D
_______ 25.
tan 60°
tan 15°
sin 60°
sin 15°
csc 𝑥
sec 𝑥
cot 𝑥
sin 𝑥
1−cos 30°
is
sin 30°
equivalent to
tangent of half angle
2 cos 𝑥
sin 2𝑥
is equivalent to
2 cos 𝛼
2 sin 𝛼 cos 𝛼
If sin 𝜃 = 𝑘, then the value of the expression sin 𝜃 cos 𝜃 tan 𝜃 is equivalent to
E. 1
F.
1
𝑘
G. 𝑘
H. 𝑘 2
sin 𝜃 cos 𝜃 sin 𝜃
∙
∙
= sin2 𝜃 = 𝑘 2
1
1 cos 𝜃