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The following are all angle measures (in degrees, rounded to the nearest tenth) whose sine is 0.36 .
Which is the principal value of
arcsin(0.36) ?
Choose 1 answer:
(A)
21.1^(@)
(B)
381.1^(@)
(c)
741.1^(@)
(D)
1101.1^(@)

The following are all angle measures (in degrees, rounded to the nearest tenth) whose sine is $0$ . $36$ . $\newline$ Which is the principal value of $\arcsin (0.36)$ ? $\newline$ Choose $1$ answer: $\newline$ (A) $21.1^{\circ}$ $\newline$ (B) $381.1^{\circ}$ $\newline$ (C) $741.1^{\circ}$ $\newline$ (D) $1101.1^{\circ}$

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Find trigonometric ratios using a Pythagorean or reciprocal identity

Full solution

Q. The following are all angle measures (in degrees, rounded to the nearest tenth) whose sine is

0

.

36

.

\newline

Which is the principal value of

\arcsin (0.36)

?

\newline

Choose

1

answer:

\newline

(A)

21.1^{\circ}

\newline

(B)

381.1^{\circ}

\newline

(C)

741.1^{\circ}

\newline

(D)

1101.1^{\circ}

Understand principal value concept: Understand the concept of the principal value for the arcsine function. $\newline$ The principal value of $\arcsin(x)$ is the value of the angle in the range from $-90^\circ$ to $90^\circ$ whose sine is $x$ . Since $0.36$ is positive, the principal value will be in the first quadrant, between $0^\circ$ and $90^\circ$ .
Use calculator for $\arcsin(0.36)$ : Use a calculator to find the principal value of $\arcsin(0.36)$ . By inputting the value into a calculator, we can find the principal value of $\arcsin(0.36)$ . Make sure the calculator is set to degree mode.
Verify calculator's result: Verify the calculator's result. $\newline$ After calculating, we find that the principal value of $\arcsin(0.36)$ is approximately $21.1$ degrees. This is within the expected range for the principal value.
Compare with given options: Compare the result with the given options. $\newline$ The calculated value of approximately $21.1$ degrees matches option $(A)$ . Options $(B)$ , $(C)$ , and $(D)$ are not within the range of $-90^\circ$ to $90^\circ$ , so they cannot be principal values of $\arcsin(0.36)$ .

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