Sullivan Gonzalez
09/12/2023 · Primary School
13. (a) Sketch the graph of \( y=2|\sin 2 x| \) for \( 0 \leq x \leq 2 \pi \). (b) Draw another graph on the same axes in (a) to determine the number of solutions for equation \( |\sin 2 x|=\frac{3 x}{2 \pi}-1 \) for \( 0 \leqslant x \leqslant 2 \pi \). State the number of solutions for the equation.
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(a) The graph of \( y=2|\sin 2x| \) has peaks at \( x = 0 \) and \( x = \pi \), and troughs at \( x = \frac{\pi}{2} \) and \( x = \frac{3\pi}{2} \). It is symmetrical about the \( x \)-axis.
(b) The equation \( |\sin 2x|=\frac{3x}{2\pi}-1 \) has four solutions in the interval \( 0 \leq x \leq 2\pi \).
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