Math Test 1

1. 求 \(1-\cos\theta+\mathrm{i}\sin\theta\) 的指数形式.

\[\begin{aligned} 1-\cos\theta+\mathrm{i}\sin\theta&=2\sin^2\dfrac{\theta}{2}+2\mathrm{i}\sin\dfrac{\theta}{2}\cos\dfrac{\theta}{2}\\ &=2\sin\dfrac{\theta}{2}\left(\sin\dfrac{\theta}{2}+\mathrm{i}\cos\dfrac{\theta}{2}\right)\\ &=2\sin\dfrac{\theta}{2}\left(\cos\dfrac{\pi-\theta}{2}+\mathrm{i}\sin\dfrac{\pi-\theta}{2}\right)\\ &=2\sin\dfrac{\theta}{2}\mathrm{e}^{\mathrm{i}\frac{\pi-\theta}{2}} \end{aligned} \]

笔记 page 6 例 1.6.

标签：cos,dfrac,Test,theta,pi,sin,Math,mathrm
来源： https://www.cnblogs.com/hl-fc/p/16350395.html