The following are all angle measures (in radians, rounded to the nearest hundredth) whose sine is -0.22 . Which is the principal value of sin^(-1)(-0.22)? Choose 1 answer: (A) -0.22 (B) 6.06 (c) 12.34 (D) 18.63

Calculate Inverse Sine: To find the principal value of sin^(-1)(-0.22), we need to calculate the inverse sine (also known as arcsine) of -0.22. The principal value of the inverse sine function is the angle in the range [-π/2, π/2] or [-90°, 90°] that has a sine of -0.22.Use Calculator or Software: Using a calculator or a mathematical software that can compute inverse trigonometric functions, we calculate sin^(-1)(-0.22). Make sure the calculator is set to radians if the answer is expected in radians.Verify Principal Value: After calculating, we find that sin^(-1)(-0.22) ≈ -0.22 radians. This is the principal value because it lies within the range [-π/2, π/2].Compare with Options: Now we compare the calculated value with the given options to find the correct answer. (A) -0.22 (B) 6.06 (C) 12.34 (D) 18.63 The correct answer is (A) -0.22, as it matches our calculated principal value.

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The following are all angle measures (in radians, rounded to the nearest hundredth) whose sine is -0.22 .
Which is the principal value of
sin^(-1)(-0.22)?
Choose 1 answer:
(A) -0.22
(B) 6.06
(c) 12.34
(D) 18.63

The following are all angle measures (in radians, rounded to the nearest hundredth) whose sine is $-0$ . $22$ . $\newline$ Which is the principal value of $\sin ^{-1}(-0.22) ?$ $\newline$ Choose $1$ answer: $\newline$ (A) $-0$ . $22$ $\newline$ (B) $6$ . $06$ $\newline$ (C) $12$ . $34$ $\newline$ (D) $\mathbf{1 8 . 6 3}$

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Math Problems

Grade 8

Calculate mean absolute deviation

Full solution

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

-0

22

\newline

Which is the principal value of

\sin ^{-1}(-0.22) ?

\newline

Choose

1

answer:

\newline

(A)

-0

22

\newline

(B)

6

06

\newline

(C)

12

34

\newline

(D)

\mathbf{1 8 . 6 3}

Calculate Inverse Sine: To find the principal value of $\sin^{-1}(-0.22)$ , we need to calculate the inverse sine (also known as arcsine) of $-0.22$ . The principal value of the inverse sine function is the angle in the range $[-\pi/2, \pi/2]$ or $[-90°, 90°]$ that has a sine of $-0.22$ .
Use Calculator or Software: Using a calculator or a mathematical software that can compute inverse trigonometric functions, we calculate $\sin^{-1}(-0.22)$ . Make sure the calculator is set to radians if the answer is expected in radians.
Verify Principal Value: After calculating, we find that $\sin^{-1}(-0.22) \approx -0.22$ radians. This is the principal value because it lies within the range $[-\frac{\pi}{2}, \frac{\pi}{2}]$ .
Compare with Options: Now we compare the calculated value with the given options to find the correct answer. $\newline$ (A) $-0.22$ $\newline$ (B) $6.06$ $\newline$ (C) $12.34$ $\newline$ (D) $18.63$ $\newline$ The correct answer is (A) $-0.22$ , as it matches our calculated principal value.