Question

sin [3 sin⁻¹ (0.4)] =

• A. 0.764
• B. 0.944
• C. 0.256
• D. 0.466

Answer 1

Answer: (B)

0.944

Answer 2

Let $\theta = \sin^{-1}(0.4)$, so that $\sin \theta = 0.4$. Using the triple-angle identity:

$$\sin(3\theta) = 3\sin\theta - 4\sin^3\theta$$

Substitute $\sin \theta = 0.4$:

$$\sin(3\theta) = 3(0.4) - 4(0.4)^3 = 1.2 - 4(0.064) = 1.2 - 0.256 = 0.944.$$

Brief Explanation:

• Use $\sin(3\theta) = 3\sin\theta - 4\sin^3\theta$.
• Substitute $0.4$ for $\sin\theta$ and calculate.