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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 11.\newlineWhich is the principal value of sin⁡−1(1)? \sin ^{-1}(1) ? \newlineChoose 11 answer:\newline(A) −630∘ -630^{\circ} \newline(B) −270∘ -270^{\circ} \newline(C) 90∘ 90^{\circ} \newline(D) 450∘ 450^{\circ}

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Full solution

Q. The following are all angle measures, in degrees, whose sine is 11.\newlineWhich is the principal value of sin⁡−1(1)? \sin ^{-1}(1) ? \newlineChoose 11 answer:\newline(A) −630∘ -630^{\circ} \newline(B) −270∘ -270^{\circ} \newline(C) 90∘ 90^{\circ} \newline(D) 450∘ 450^{\circ}
  1. Principal Value Definition: The principal value of the inverse sine function, sin⁡−1(x)\sin^{-1}(x), is the value in the range [−90°,90°][-90°, 90°] or [−π2,π2][-\frac{\pi}{2}, \frac{\pi}{2}] in radians.
  2. Sine of 9090°: Since the sine of 90°90° is 11, and 90°90° is within the range of the principal values for the inverse sine function, sin⁡−1(1)=90°\sin^{-1}(1) = 90°.
  3. Correct Answer: Looking at the options provided, (C) 90°90° is the correct answer because it is the only option within the principal range [−90°,90°][-90°, 90°].

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