Q. What is the range of the function y = cos^(-1)(x)?
A.
[0, π]
B.
[0, 2π]
C.
[−π/2, π/2]
D.
[−1, 1]
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Solution
The range of y = cos^(-1)(x) is [0, π].
Correct Answer: A — [0, π]
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Q. What is the range of the function y = sin^(-1)(x)?
A.
[-π/2, π/2]
B.
[0, π]
C.
[-1, 1]
D.
[0, 1]
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Solution
The range of y = sin^(-1)(x) is [-π/2, π/2].
Correct Answer: A — [-π/2, π/2]
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Q. What is the range of the function y = tan^(-1)(x)?
A.
(-π/2, π/2)
B.
(0, π)
C.
(0, 1)
D.
(-1, 1)
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Solution
The range of the function y = tan^(-1)(x) is (-π/2, π/2).
Correct Answer: A — (-π/2, π/2)
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Q. What is the value of cos^(-1)(-1)?
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Solution
cos^(-1)(-1) = π, since cos(π) = -1.
Correct Answer: B — π
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Q. What is the value of sec(sin^(-1)(1/2))?
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Solution
sec(sin^(-1)(1/2)) = 1/cos(π/6) = 2.
Correct Answer: B — 2
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Q. What is the value of sec(sin^(-1)(3/5))?
A.
5/3
B.
√(34)/3
C.
√(34)/5
D.
3/5
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Solution
sec(sin^(-1)(3/5)) = √(34)/3
Correct Answer: B — √(34)/3
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Q. What is the value of sec(tan^(-1)(1/√3))?
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Solution
Using the triangle with opposite = 1 and adjacent = √3, hypotenuse = 2. Thus, sec(tan^(-1)(1/√3)) = 2.
Correct Answer: A — 2
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Q. What is the value of sin(tan^(-1)(x))?
A.
x/√(1+x^2)
B.
√(1+x^2)/x
C.
1/x
D.
x
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Solution
sin(tan^(-1)(x)) = x/√(1+x^2)
Correct Answer: A — x/√(1+x^2)
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Q. What is the value of sin^(-1)(1/2) + cos^(-1)(1/2)?
A.
π/3
B.
π/2
C.
π/6
D.
π/4
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Solution
sin^(-1)(1/2) = π/6 and cos^(-1)(1/2) = π/3. Therefore, sin^(-1)(1/2) + cos^(-1)(1/2) = π/6 + π/3 = π/2.
Correct Answer: B — π/2
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Q. What is the value of sin^(-1)(1/2) + sin^(-1)(√3/2)?
A.
π/3
B.
π/2
C.
2π/3
D.
π
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Solution
sin^(-1)(1/2) = π/6 and sin^(-1)(√3/2) = π/3. Therefore, π/6 + π/3 = π/2.
Correct Answer: B — π/2
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Q. What is the value of sin^(-1)(1/2)?
A.
π/6
B.
π/4
C.
π/3
D.
π/2
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Solution
sin^(-1)(1/2) = π/6, since sin(π/6) = 1/2.
Correct Answer: A — π/6
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Q. What is the value of tan^(-1)(1) + tan^(-1)(1)?
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Solution
tan^(-1)(1) = π/4, thus tan^(-1)(1) + tan^(-1)(1) = π/4 + π/4 = π/2.
Correct Answer: A — π/2
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Q. What is the value of tan^(-1)(1) + tan^(-1)(2)?
A.
π/4
B.
π/3
C.
π/2
D.
π/6
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Solution
Using the formula tan^(-1)(a) + tan^(-1)(b) = tan^(-1)((a+b)/(1-ab)), we have tan^(-1)(1) + tan^(-1)(2) = tan^(-1)((1+2)/(1-1*2)) = tan^(-1)(3/-1) = π - tan^(-1)(3) = π/4.
Correct Answer: A — π/4
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Q. What is the value of tan^(-1)(1)?
A.
π/4
B.
π/3
C.
π/2
D.
0
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Solution
tan^(-1)(1) = π/4, since tan(π/4) = 1.
Correct Answer: A — π/4
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