Answer to Question #144320 in Trigonometry for Shahir Sheikh

Question

If sec(α)<0 and the sin(α)=15/17

What is the exact value of cot(α)

Answer 1

$sec(\alpha)=\frac 1 {cos(\alpha)}$ . if $sec(\alpha)<0$ then $cos(\alpha)<0$ .

$cos(\alpha)=-\sqrt{1-sin^{2}(\alpha)}=-\sqrt{1-(\frac {15} {19})^{2}}=-\sqrt{\frac{64} {289}}=-\frac 8 {17}$

$cot(\alpha)=\frac {cos(\alpha)} {sin(\alpha)}=-\frac 8 {15}$