Trigonometry & Inverse Trigonometry
Trigonometric Functions
Grade 11
Question:
<p>If \(f(x) = \sin^2 x + \sin^2\left(x + \frac{2\pi}{3}\right) + \sin^2\left(x + \frac{4\pi}{3}\right)\) then:</p>
<p>(a) \(f\left(\frac{\pi}{15}\right) = \frac{3}{2}\)</p>
<p>(b) \(f\left(\frac{15}{\pi}\right) = \frac{2}{3}\)</p>
<p>(c) \(f\left(\frac{\pi}{10}\right) = \frac{3}{2}\)</p>
<p>(d) \(f\left(\frac{10}{\pi}\right) = \frac{2}{3}\)</p>
Step-by-Step Solution
Key Concept: The function is periodic and simplifies to a constant using trigonometric identities.
<p>Using sum formulas and simplification, the function reduces to a constant value of \(\frac{3}{2}\) for all \(x\).</p>
Correct Answer: a, c