Question

вычислить : 2)соs(a), tg (a) ctg(a) если sin (a)= -2/5 и П<(а)<3П/2

Answer 1

$\cos\alpha=\sqrt{1-\sin^2\alpha}=\sqrt{1-\frac4{25}}=\sqrt{\frac{21}{25}}=\pm\frac{\sqrt{21}}5\\\pi\ \textless \ \alpha\ \textless \ \frac{3\pi}2\Rightarrow\cos\alpha\ \textless \ 0\\\cos\alpha=-\frac{\sqrt{21}}5\\tg\alpha=\frac{\sin\alpha}{\cos\alpha}=\left(-\frac25\right):\left(-\frac{\sqrt{21}}5\right)=\frac25\cdot\frac5{\sqrt{21}}=\frac2{\sqrt{21}}\\ctg\alpha=\frac1{tg\alpha}=\frac{\sqrt{21}}2$