Question

Найдите значения sin , tga , ctga . известно , что cosa=4/5 и 3пи/2

Answer 1

$\cos\alpha=\frac45,\;\;\;\frac{3\pi}2<\alpha<2\pi\\\sin^2\alpha+\cos^2\alpha=1\Rightarrow\sin\alpha=\sqrt{1-\cos^2\alpha}\\\sin\alpha=\sqrt{1-\left(\frac45\right)^2}=\sqrt{1-\frac{16}{25}}=\sqrt{\frac9{25}}=\pm\frac35\\\frac{3\pi}2<\alpha<2\pi\Rightarrow\sin\alpha<0\\\sin\alpha=-\frac34\\tg\alpha=\frac{\sin\alpha}{\cos\alpha}=\frac35:\frac45=\frac35\cdot\frac54=\frac34\\\\ctg\alpha=\frac1{tg\alpha}=\frac43=1\frac13$