Trigonometry & Inverse Trigonometry
Inverse Trigonometric Functions
Grade 12
Question:
<p>If $\frac{x + \frac{3}{x}}{} = 2$, then the value of $\sin^{-1} x$ is</p>
<p>(a) $\frac{\pi}{4}$</p>
<p>(b) $\frac{\pi}{2}$</p>
<p>(c) $\pi$</p>
<p>(d) $\frac{3\pi}{2}$</p>
Step-by-Step Solution
Key Concept: Solve the given equation for $x$, then find its inverse sine value.
Step 1: The value of $x$ is $\frac{1}{\sqrt{2}}$.
Step 2: Calculate $\sin^{-1} x$.
$$ \sin^{-1} x = \sin^{-1}\left(\frac{1}{\sqrt{2}}\right) = \frac{\pi}{4} $$
Correct Answer: A