Question

\(\sin\!\big(\sin^{-1}\tfrac12\big)=\) ?

• A. \(1\)
• B. \(\tfrac12\)
• C. \(\tfrac{\sqrt3}{2}\)
• D. \(0\)

Hint:

For any \(x\in[-1,1]\), \(\sin(\sin^{-1}x)=x\).

Answer 1

The Correct Option is B

\(\sin^{-1}\) returns an angle whose sine is the input. Thus \(\theta=\sin^{-1}\tfrac12\) satisfies \(\sin\theta=\tfrac12\). Applying \(\sin\) undoes \(\sin^{-1}\): \[ \sin(\sin^{-1}\tfrac12)=\tfrac12. \]