Q. If sin(x) = 0.5, what are the possible values of x in degrees?
-
A.
30°, 150°
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B.
45°, 135°
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C.
60°, 120°
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D.
90°, 270°
Solution
sin(x) = 0.5 gives x = 30° and 150°.
Correct Answer:
A
— 30°, 150°
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Q. If sin(x) = 0.8, what is the value of csc(x)?
-
A.
0.8
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B.
1.25
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C.
1.2
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D.
0.5
Solution
csc(x) = 1/sin(x) = 1/0.8 = 1.25.
Correct Answer:
B
— 1.25
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Q. If tan(x) = 1, what is the value of x in the interval [0°, 360°)?
-
A.
45°
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B.
135°
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C.
225°
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D.
315°
Solution
tan(x) = 1 at x = 45° and 225°; in the interval [0°, 360°), the first solution is 45°.
Correct Answer:
A
— 45°
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Q. Solve for x: 2sin(x) = √3, where 0 ≤ x < 360°.
-
A.
30°
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B.
150°
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C.
210°
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D.
330°
Solution
sin(x) = √3/2 gives x = 60° and 120°, so 2sin(x) = √3 gives x = 150°.
Correct Answer:
B
— 150°
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Q. Solve for x: cos(x) = 0.5, where 0 ≤ x < 360°.
-
A.
60°
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B.
120°
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C.
240°
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D.
300°
Solution
cos(x) = 0.5 gives x = 60° and 300°.
Correct Answer:
A
— 60°
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Q. What is the value of cos(45°)?
-
A.
0
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B.
1/2
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C.
√2/2
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D.
√3/2
Solution
cos(45°) = √2/2.
Correct Answer:
C
— √2/2
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Q. Which equation represents the double angle identity for sine?
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A.
sin(2x) = 2sin(x)cos(x)
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B.
sin(2x) = sin²(x) + cos²(x)
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C.
sin(2x) = sin(x) + cos(x)
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D.
sin(2x) = 2sin²(x)
Solution
The double angle identity for sine is sin(2x) = 2sin(x)cos(x).
Correct Answer:
A
— sin(2x) = 2sin(x)cos(x)
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Q. Which of the following is a Pythagorean identity?
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A.
sin²x + cos²x = 1
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B.
tanx = sinx/cosx
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C.
secx = 1/cosx
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D.
cscx = 1/sinx
Solution
The Pythagorean identity is sin²x + cos²x = 1.
Correct Answer:
A
— sin²x + cos²x = 1
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Q. Which of the following is the correct expression for cot(x)?
-
A.
cos(x)/sin(x)
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B.
1/tan(x)
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C.
sin(x)/cos(x)
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D.
tan(x)/1
Solution
cot(x) = 1/tan(x) = cos(x)/sin(x).
Correct Answer:
B
— 1/tan(x)
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Q. Which of the following is the correct identity for cotangent?
-
A.
cot(x) = cos(x)/sin(x)
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B.
cot(x) = sin(x)/cos(x)
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C.
cot(x) = 1/tan(x)
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D.
cot(x) = tan(x)/1
Solution
cot(x) = cos(x)/sin(x) is the correct identity.
Correct Answer:
A
— cot(x) = cos(x)/sin(x)
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