Question

The values of $cos\alpha ,tan\alpha ,cot\alpha ,$ respectively if $sin\alpha =\frac{5}{13}$ and $\frac{\pi }{2}<\alpha <\pi$

• A. $-\frac{12}{13},-\frac{5}{12},-\frac{12}{5}$
• B. $-\frac{12}{13},-\frac{5}{13},-\frac{13}{5}$
• C. $-\frac{12}{5},-\frac{5}{12},-\frac{12}{5}$
• D. $-\frac{12}{13},-\frac{5}{13},-\frac{13}{5}$

Answer 1

The correct option is A $-\frac{12}{13},-\frac{5}{12},-\frac{12}{5}$

$cos\alpha =-\sqrt{(1-si{n}^2\alpha )}=-\frac{12}{13}$
$tan\alpha =\frac{sin\alpha }{cos\alpha }=-\frac{5}{12}$
$cot\alpha =\frac{1}{tan\alpha }=-\frac{12}{5}$