문제 원리

• 삼각함수 공식

$$\sin(\alpha) \cdot \sin(\beta) = - \dfrac{1}{2}[\cos (\alpha + \beta) - \cos (\alpha - \beta)]$$

$$\begin{aligned} \sin(\omega t + 30^\circ) \cdot \sin(\omega t + 60^\circ) &= - \dfrac{1}{2}[\cos (2\omega t +30^\circ + 60^\circ) - \cos ( 30^\circ - 60^\circ)]\\ &= \dfrac{1}{2} \dfrac{\sqrt3}{2} \end{aligned}$$

$$\begin{aligned} P_0 &= V \times I_0 = 200 \sin(\omega t + 30^\circ) \times 3 \sin (\omega t + 60 ) \\&= 600 \dfrac{\sqrt3}{4}= 259.807\end{aligned}$$