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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 −0-0.2222 .\newlineWhich is the principal value of sin⁡−1(−0.22)? \sin ^{-1}(-0.22) ? \newlineChoose 11 answer:\newline(A) −0-0.2222\newline(B) 66.0606\newline(C) 1212.3434\newline(D) 18.63 \mathbf{1 8 . 6 3}

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Q. The following are all angle measures (in radians, rounded to the nearest hundredth) whose sine is −0-0.2222 .\newlineWhich is the principal value of sin⁡−1(−0.22)? \sin ^{-1}(-0.22) ? \newlineChoose 11 answer:\newline(A) −0-0.2222\newline(B) 66.0606\newline(C) 1212.3434\newline(D) 18.63 \mathbf{1 8 . 6 3}
  1. Calculate Inverse Sine: To find the principal value of sin⁡−1(−0.22)\sin^{-1}(-0.22), we need to calculate the inverse sine (also known as arcsine) of −0.22-0.22. The principal value of the inverse sine function is the angle in the range [−π/2,π/2][-\pi/2, \pi/2] or [−90°,90°][-90°, 90°] that has a sine of −0.22-0.22.
  2. Use Calculator or Software: Using a calculator or a mathematical software that can compute inverse trigonometric functions, we calculate sin⁡−1(−0.22)\sin^{-1}(-0.22). Make sure the calculator is set to radians if the answer is expected in radians.
  3. Verify Principal Value: After calculating, we find that sin⁡−1(−0.22)≈−0.22\sin^{-1}(-0.22) \approx -0.22 radians. This is the principal value because it lies within the range [−π2,π2][-\frac{\pi}{2}, \frac{\pi}{2}].
  4. Compare with Options: Now we compare the calculated value with the given options to find the correct answer.\newline(A) −0.22-0.22\newline(B) 6.066.06\newline(C) 12.3412.34\newline(D) 18.6318.63\newlineThe correct answer is (A) −0.22-0.22, as it matches our calculated principal value.

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