Chapter 6 - Analytic Trigonometry - Section 6.6 Double-angle and Half-angle Formulas - 6.6 Assess Your Understanding - Page 519: 93

$\frac{\pi}{2},\frac{3\pi}{2}$

1. Let $f(x)=0$ or $cos(2x)+sin^2(x)=0\Longrightarrow 1-2sin^2(x)+sin^2(x)=0\Longrightarrow sin^2(x)=1\Longrightarrow sin(x)=\pm1$ 2. For $sin(x)=1$, we have $x=2k\pi+\frac{\pi}{2}$. 3. For $sin(x)=-1$, we have $x=2k\pi+\frac{3\pi}{2}$. 4. Within $[0,2\pi)$, we have $\theta=\frac{\pi}{2},\frac{3\pi}{2}$