Trig Equations Multiple Choice
__________ 1.
sin 𝑥
For what value(s) of x is the expression 1+cos 𝑥 undefined?
A. 0
B. 60
C. 90
__________ 2.
D. 180
E. 270
1
In the interval 0 ≤ 𝑥 < 360° how many values of 𝑥 satisfy the equation sin2 𝑥 = 4?
A. 1
B. 2
__________ 3.
C. 3
D. 4
sin2 𝑥
For what value(s) of 𝑥 is the expression 1−sin2 𝑥 undefined?
A. 0
B. 45 and 90
__________ 4.
C. 90 and 270
D. 180
E. Never
For what value of 𝑏 is sin(𝑥 + 𝑏) = cos 𝑥?
A.
3𝜋
2
D.
𝜋
E. 2𝜋
B. − 2
__________ 5.
__________ 6.
__________ 7.
__________ 8.
𝜋
2
C. – 𝜋
How many solutions are there in the interval 0 ≤ 𝑥 < 2𝜋 for the equation 3 cos 2𝑥 = −3?
A. 0
D. 3
B. 1
E. 4
C. 2
In the interval 0 ≤ 𝑥 < 2𝜋, how many values of 𝑥 satisfy the equation 3 sin2 𝑥 + sin 𝑥 − 2 = 0?
A. 0
D. 3
B. 1
E. 4
C. 2
How many solutions are there in the interval 0 ≤ 𝑥 < 2𝜋 for the equation 3 cos 2𝑥 = −5?
A. 0
D. 3
B. 1
E. 4
C. 2
What value of 𝑥 does not satisfy the equation sin2 𝑥 + sin 𝑥 = 0?
𝜋
3𝜋
A. 2
C.
2
__________ 9.
__________ 10.
__________ 11.
B. 𝜋
D. 2𝜋
How many solutions are there in the interval 0 ≤ 𝑥 < 2𝜋 for the equation 3 cos 2𝑥 = −1?
A. 0
D. 3
B. 1
E. 4
C. 2
In the interval 0 ≤ 𝑥 < 360°, for what value of 𝑥 does sin 𝑥 = cos 𝑥?
A. 45 only
C. 135 and 315
B. 45 and 225
D. 225 only
A solution of the equation √4 sin 𝑥 + 7 = 3 is
𝜋
𝜋
A. 4
C. 6
B.
__________ 12.
𝜋
3
D.
sin2 𝑥
𝜋
2
For what value(s) of 𝑥 is the expression 1+sin2 𝑥 undefined?
A. 45
B. 90
C. 180
D. 270
E. Never
__________ 13.
__________ 14.
__________ 15.
__________ 16.
How many solutions are there in the interval 0 ≤ 𝑥 < 2𝜋 for the equation 4 cos 3𝑥 = 1?
A. 0
E. 4
B. 1
F. 5
C. 2
G. 6
D. 3
How many solutions are there in the interval 0 ≤ 𝑥 < 2𝜋 for the equation 4 cos 3𝑥 = 4?
A. 0
E. 4
B. 1
F. 5
C. 2
G. 6
D. 3
How many solutions are there in the interval 0 ≤ 𝑥 < 2𝜋 for the equation 4 cos 3𝑥 = 9?
A. 0
E. 4
B. 1
F. 5
C. 2
G. 6
D. 3
7𝜋
If 𝑓(𝑥) = 5 cos(2𝑥) − 3 then what is the value of 𝑓 ( 6 )?
5𝜋
D. cos ( 6 )
B. sin (−
E. sin (−
C.
__________ 17.
__________ 18.
__________ 19.
__________ 20.
__________ 21.
__________ 22.
__________ 23.
7𝜋
A. cos ( 6 )
5𝜋
)
6
7𝜋
sin (− )
6
What is one possible value of 𝑥 that satisfies the equation cot 𝑥
A. 0
B. 45
What is one solution of the equation (sin 𝑥 + cos 𝑥)2 = 2?
𝜋
A.
= cos 𝑥?
C. 90
D. 180
B.
D. 0
4
𝜋
3
A solution of the equation cos 2𝑥 + sin 2𝑥 = −1 is
A. 240
B. 135
For what value of 𝑥 is the expression
2 sin 𝑥
tan 𝑥
𝜋
2
C. 45
D. –30
undefined?
A. 0 only
B. 45 only
C. 90 only
Which two values of 𝑥 satisfy the equation √3 − 2 cos 𝑥 = 2?
A. 150 and 210
B. 120 and 240
For what value(s) of 𝑥 is the expression
C.
5𝜋
)
3
2
sec 𝑥
D. 0 and 180
E. 45 and 225
F. 90 and 270
C. 60 and 300
D. 30 and 330
undefined?
A. 45
D. 270
E. Never
B. 90
C. 180
How many solutions are there in the interval 0 ≤ 𝑥 < 2𝜋 for the equation 2 cos 5𝑥 = 9?
A. 0
G. 6
B. 1
H. 7
C. 2
I. 8
D. 3
J. 9
E. 4
K. 10
F. 5
__________ 24.
__________ 25.
How many solutions are there in the interval 0 ≤ 𝑥 < 2𝜋 for the equation 2 cos 5𝑥 = 0.5?
A. 0
G. 6
B. 1
H. 7
C. 2
I. 8
D. 3
J. 9
E. 4
K. 10
F. 5
How many solutions are there in the interval 0 ≤ 𝑥 < 2𝜋 for the equation 2 cos 5𝑥 = 2?
A. 0
G. 6
B. 1
H. 7
C. 2
I. 8
D. 3
J. 9
E. 4
K. 10
F. 5
Trig Equations Multiple Choice
D
__________
1.
sin 𝑥
For what value(s) of x is the expression 1+cos 𝑥 undefined?
A. 0
B. 60
C. 90
D. 180
E. 270
1 + cos 𝑥 = 0
cos 𝑥 = −1
1
D
__________
2.
In the interval 0 ≤ 𝑥 < 360° how many values of 𝑥 satisfy the equation sin2 𝑥 = 4?
1
A. 1
C. 3
sin 𝑥 = ±
2
B. 2
D. 4
C
__________
3.
For what value(s) of 𝑥 is the expression 1−sin2 𝑥 undefined?
sin2 𝑥
A. 0
B. 45 and 90
D
__________
4.
C. 90 and 270
D. 180
E. Never
1 − sin2 𝑥 = 0
sin 𝑥 = ±1
For what value of 𝑏 is sin(𝑥 + 𝑏) = cos 𝑥?
A.
3𝜋
2
2
D.
𝜋
B. − 2
𝜋
2
E. 2𝜋
3π
C. – 𝜋
How many solutions are there in the interval 0 ≤ 𝑥 < 2𝜋 for the equation 3 cos 2𝑥 = −3?
A. 0
D. 3
B. 1
E. 4
C. 2
In the interval 0 ≤ 𝑥 < 2𝜋, how many values of 𝑥 satisfy the equation 3 sin2 𝑥 + sin 𝑥 − 2 = 0?
A. 0
D. 3
(3 sin 𝑥 − 2)(sin 𝑥 + 1) = 0
B. 1
2
E. 4
sin 𝑥 = 3 or sin 𝑥 = −1
C. 2
How many solutions are there in the interval 0 ≤ 𝑥 < 2𝜋 for the equation 3 cos 2𝑥 = −5?
A. 0
D. 3
B. 1
E. 4
C. 2
What value of 𝑥 does not satisfy the equation sin2 𝑥 + sin 𝑥 = 0?
𝜋
3𝜋
(sin 𝑥)(sin 𝑥 + 1) = 0
A. 2
C. 2
sin 𝑥 = 0 or sin 𝑥 = −1
B. 𝜋
D. 2𝜋
2
C
__________
5.
2
2π
2
4
D
__________
6.
A
__________
7.
2π
5
A
__________
8.
E
__________
9.
How many solutions are there in the interval 0 ≤ 𝑥 < 2𝜋 for the equation 3 cos 2𝑥 = −1?
A. 0
D. 3
B. 1
E. 4
C. 2
In the interval 0 ≤ 𝑥 < 360°, for what value of 𝑥 does sin 𝑥 = cos 𝑥?
A. 45 only
C. 135 and 315
B. 45 and 225
D. 225 only
A solution of the equation √4 sin 𝑥 + 7 = 3 is
𝜋
𝜋
A. 4
C. 6
4 sin 𝑥 + 7 = 9
2π
B
__________
10.
C
__________
11.
B.
E
__________
12.
𝜋
3
1
sin 𝑥 = 2
D.
sin2 𝑥
𝜋
2
For what value(s) of 𝑥 is the expression 1+sin2 𝑥 undefined?
A. 45
B. 90
1 + sin2 𝑥 = 0
sin 𝑥 = imaginary
C. 180
D. 270
E. Never
G
__________
13.
How many solutions are there in the interval 0 ≤ 𝑥 < 2𝜋 for the equation 4 cos 3𝑥 = 1?
A. 0
E. 4
B. 1
F. 5
C. 2
G. 6
D. 3
How many solutions are there in the interval 0 ≤ 𝑥 < 2𝜋 for the equation 4 cos 3𝑥 = 4?
A. 0
E. 4
B. 1
F. 5
C. 2
G. 6
D. 3
How many solutions are there in the interval 0 ≤ 𝑥 < 2𝜋 for the equation 4 cos 3𝑥 = 9?
A. 0
E. 4
B. 1
F. 5
C. 2
G. 6
D. 3
2π
D
__________
14.
5
2π
5
A
__________
15.
10
5
2π
B
__________
16.
7𝜋
If 𝑓(𝑥) = 5 cos(2𝑥) − 3 then what is the value of 𝑓 ( 6 )?
5𝜋
A. cos ( 6 )
5𝜋
)
6
7𝜋
sin (− )
6
B. sin (−
C.
7𝜋
7𝜋
) − 3 = 5 cos ( ) − 3
6
3
1
1
= 5( ) − 3 = −
2
2
5 cos (2 ∙
7𝜋
D. cos ( 6 )
E. sin (−
C
__________
17.
What is one possible value of 𝑥 that satisfies the equation cot 𝑥 = cos 𝑥?
cos 𝑥
A. 0
C. 90
− cos 𝑥 = 0
sin
𝑥
B. 45
D. 180
cos 𝑥 − cos 𝑥 sin 𝑥 = 0
cos 𝑥 (1 − sin 𝑥) = 0
cos 𝑥 = 0 or sin 𝑥 = 1
A
__________
18.
What is one solution of the equation (sin 𝑥 + cos 𝑥)2 = 2?
𝜋
1 + 2 sin 𝑥 cos 𝑥 = 2
A. 4
𝜋
sin 2𝑥 = 1
B.
C.
A solution of the equation cos 2𝑥 + sin 2𝑥 = −1 is
2 cos 2 𝑥 − 1 + 2 sin 𝑥 cos 𝑥 = −1
A. 240
2 cos2 𝑥 + 2 sin 𝑥 cos 𝑥 = 0
B. 135
2 cos 𝑥 (cos 𝑥 + sin 𝑥) = 0
C. 45
D. –30
3
B
__________
19.
2 sin 𝑥
tan 𝑥
5𝜋
)
3
𝜋
2
D. 0
D
__________
20.
For what value of 𝑥 is the expression
D. 0 and 180
E. 45 and 225
F. 90 and 270
B
__________
21.
A. 0 only
tan 𝑥 = 0
B. 45 only
C. 90 only
Which two values of 𝑥 satisfy the equation √3 − 2 cos 𝑥 = 2?
3 − 2 cos 𝑥 = 4
A. 150 and 210
1
B. 120 and 240
cos 𝑥 = − 2
2
For what value(s) of 𝑥 is the expression sec 𝑥 undefined?
A. 45
B. 90
C. 180
D. 270
E. Never
E
__________
22.
sec 𝑥 = 0
undefined?
C. 60 and 300
D. 30 and 330
A
__________
23.
How many solutions are there in the interval 0 ≤ 𝑥 < 2𝜋 for the equation 2 cos 5𝑥 = 9?
A. 0
G. 6
B. 1
H. 7
C. 2
I. 8
D. 3
J. 9
E. 4
K. 10
F. 5
How many solutions are there in the interval 0 ≤ 𝑥 < 2𝜋 for the equation 2 cos 5𝑥 = 0.5?
A. 0
G. 6
B. 1
H. 7
C. 2
I. 8
D. 3
J. 9
E. 4
K. 10
F. 5
How many solutions are there in the interval 0 ≤ 𝑥 < 2𝜋 for the equation 2 cos 5𝑥 = 2?
A. 0
G. 6
B. 1
H. 7
C. 2
I. 8
D. 3
J. 9
E. 4
K. 10
F. 5
10
5
π
K
__________
24.
π
F
__________
25.
π
2π
2π
2π