Find the value of sin⁻¹(3x - 4x³) at x = 0.3 and at x = 0.8, in radians…

Step 1. At $x = 0.3$. The number is inside $|x| \le \dfrac{1}{2}$. So $\sin^{-1}(3x - 4x^3) = 3\sin^{-1}0.3 = 3 \times 0.3047 = 0.9141$. Directly: $3(0.3) - 4(0.027) = 0.792$ and $\sin^{-1}0.792 = 0.9141$.

Step 2. At $x = 0.8$. The number is above $\dfrac{1}{2}$, so $3\sin^{-1}0.8 = 2.7819$ is not the value, because it is above $\dfrac{\pi}{2}$. The value is $\pi - 3\sin^{-1}0.8 = 3.1416 - 2.7819 = 0.3597$. Directly: $3(0.8) - 4(0.512) = 0.352$ and $\sin^{-1}0.352 = 0.3597$.