Question

The value of $\sin(2 \sin^{-1} 0.8)$ is:

• A. 0.96
• B. 0.48
• C. 0.64
• D. 0.32

Hint:

If $\sin \theta = 4/5$, then $\cos \theta = 3/5$ (3-4-5 triangle).

Answer 1

The Correct Option is A

Step 1: Concept
Use the identity $\sin(2\theta) = 2 \sin \theta \cos \theta$.
Step 2: Analysis
Let $\sin^{-1} 0.8 = \theta$. Then $\sin \theta = 0.8$. Using $\cos \theta = \sqrt{1 - \sin^{2} \theta} = \sqrt{1 - 0.64} = \sqrt{0.36} = 0.6$. $\sin(2\theta) = 2(0.8)(0.6)$.
Step 3: Conclusion
$\sin(2\theta) = 2(0.48) = 0.96$.
Final Answer: (A)