Question

If sin(theta) =4/5 and is in quadrant 2, the value of cot(theta

Answer 1

$\sin\theta= \frac{4}{5} \\ \\\sin^2\theta+\cos^2\theta=1 \\ \cos\theta=\pm \sqrt{1-\sin^2\theta} =\pm \sqrt{1-( \frac{4}{5})^2 } =\pm \sqrt{1- \frac{16}{25} } =\pm \sqrt{\frac{9}{25} }=\pm \frac{3}{5}}$

$\theta \in II \Rightarrow \cos\theta\ \textless \ 0 \Rightarrow \cos\theta=-\frac{3}{5}$

$\cot\theta= \frac{\cos\theta}{\sin\theta}= \frac{-\frac{3}{5}}{\frac{4}{5}} =- \frac{3}{4}$