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The following are all angle measures (in degrees, rounded to the nearest tenth) whose sine is -0.71 .
Which is the principal value of
arcsin(-0.71) ?
Choose 1 answer:
(A)
-405.2^(@)
(B)
-45.2^(@)
(c)
314.8^(@)
(D)
674.8^(@)

The following are all angle measures (in degrees, rounded to the nearest tenth) whose sine is $-0$ . $71$ . $\newline$ Which is the principal value of $\arcsin (-0.71)$ ? $\newline$ Choose $1$ answer: $\newline$ (A) $-405.2^{\circ}$ $\newline$ (B) $-45.2^{\circ}$ $\newline$ (C) $314.8^{\circ}$ $\newline$ (D) $674.8^{\circ}$

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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

.

71

.

\newline

Which is the principal value of

\arcsin (-0.71)

?

\newline

Choose

1

answer:

\newline

(A)

-405.2^{\circ}

\newline

(B)

-45.2^{\circ}

\newline

(C)

314.8^{\circ}

\newline

(D)

674.8^{\circ}

Define Principal Value: The principal value of $\text{arcsin}(x)$ is the value of the inverse sine function that lies in the range $-90°$ to $90°$ .
Identify Quadrant: Since the sine function is negative in the third and fourth quadrants, and the principal value must be between $-90°$ and $90°$ , we are looking for an angle in the fourth quadrant.
Calculate Inverse Sine: To find the principal value of $\arcsin(-0.71)$ , we can use a calculator or inverse sine function to find the angle whose sine is $-0.71$ .
Use Calculator: Using a calculator, we find that $\arcsin(-0.71) \approx -45.2^\circ$ .
Determine Principal Value: Therefore, the principal value of $\arcsin(-0.71)$ is $-45.2^\circ$ , which corresponds to option (B).

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