The following are all angle measures, in degrees, whose sine is 1. Which is the principal value of sin^(-1)(1) ? Choose 1 answer: (A) -630^(@) (B) -270^(@) (C) 90^(@) (D) 450^(@)

Principal Value Definition: The principal value of the inverse sine function, sin^(-1)(x), is the value in the range [-90°, 90°] or [-π/2, π/2] in radians.Sine of 90°: Since the sine of 90° is 1, and 90° is within the range of the principal values for the inverse sine function, sin^(-1)(1) = 90°.Correct Answer: Looking at the options provided, (C) 90° is the correct answer because it is the only option within the principal range [-90°, 90°].

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The following are all angle measures, in degrees, whose sine is 1.
Which is the principal value of
sin^(-1)(1) ?
Choose 1 answer:
(A)
-630^(@)
(B)
-270^(@)
(C)
90^(@)
(D)
450^(@)

The following are all angle measures, in degrees, whose sine is $1$ . $\newline$ Which is the principal value of $\sin ^{-1}(1) ?$ $\newline$ Choose $1$ answer: $\newline$ (A) $-630^{\circ}$ $\newline$ (B) $-270^{\circ}$ $\newline$ (C) $90^{\circ}$ $\newline$ (D) $450^{\circ}$

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Math Problems

Algebra 2

Inverses of csc, sec, and cot

Full solution

Q. The following are all angle measures, in degrees, whose sine is

1

\newline

Which is the principal value of

\sin ^{-1}(1) ?

\newline

Choose

1

answer:

\newline

(A)

-630^{\circ}

\newline

(B)

-270^{\circ}

\newline

(C)

90^{\circ}

\newline

(D)

450^{\circ}

Principal Value Definition: The principal value of the inverse sine function, $\sin^{-1}(x)$ , is the value in the range $[-90°, 90°]$ or $[-\frac{\pi}{2}, \frac{\pi}{2}]$ in radians.
Sine of $90$ °: Since the sine of $90°$ is $1$ , and $90°$ is within the range of the principal values for the inverse sine function, $\sin^{-1}(1) = 90°$ .
Correct Answer: Looking at the options provided, (C) $90°$ is the correct answer because it is the only option within the principal range $[-90°, 90°]$ .