Trigonometry & Inverse Trigonometry
Trigonometric Equations
Grade 11
Question:
<p>The number of points in interval \(\left[-\frac{\pi}{2}, \frac{\pi}{2}\right]\) where the graphs of the curves \(y = \cos x\) and \(y = \sin 3x\), with \(-\frac{\pi}{2} \le x \le \frac{\pi}{2}\), intersect is:</p>
Step-by-Step Solution
Key Concept: Convert \(\sin 3x\) to cosine form and use the solution formula for \(\cos A = \cos B\).
<p>Solve \(\cos x = \sin 3x\) in the given interval. Rewrite as \(\cos x = \cos\left(\frac{\pi}{2} - 3x\right)\) and apply the general solution for cosine equality. Verify solutions graphically or by substitution in the interval.</p>
Correct Answer: 3