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★ 7/10trigonometry Trigonometric Identities Casework

Problem

Let

f(x)=\sin^2\frac{\omega x}2+\frac 12\sin\omega x-\frac 12\qquad(\omega>0),\quad x\in\mathbb R.

Suppose $f(x)$ has no zero in the interval $(\pi,2\pi)$ . Find the range of $\omega$ .

Answer

Solution

Difficulty	7/10
Topics	trigonometry, Trigonometric Identities, Casework

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