E-EQ01 · Transform the interval as well as the angle
Solve \(\displaystyle \sin(2x+\frac\pi3)=\frac{\sqrt3}{2}\), subject to \(\displaystyle -\frac\pi2\le x\le\pi\).
With \(\displaystyle u=2x+\frac\pi3\), state the full interval for \(u\).
Find all permitted \(u\), then all \(x\) satisfying the equation.
How does the solution set change if the interval becomes \(\displaystyle - \frac{\pi }{2}\lt x\lt \pi\)? Explain.
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