Tobias Ali

## Answered question

2021-08-15

If $\mathrm{tan}=\frac{-4}{3}$ and $3\cdot \frac{\pi }{2}, find $\mathrm{sin}t,\mathrm{cos}t,\mathrm{sec}t,\mathrm{csc}t,\mathrm{cot}t$.

### Answer & Explanation

Anonym

Skilled2021-08-16Added 108 answers

We have to find the trigonometry ratios

${\mathrm{sec}}^{2}t=1+{\mathrm{tan}}^{2}t=1+\frac{16}{9}=\frac{25}{9}$
$\mathrm{sec}t=\sqrt{\frac{25}{9}}=±\frac{5}{3}$
$\mathrm{sec}t=\frac{5}{3}\left(\because \frac{3\pi }{2}
$\mathrm{cos}t=\frac{1}{\mathrm{sec}t}=\frac{3}{5}$
$\mathrm{sin}t=\sqrt{1-{\mathrm{cos}}^{2}t}=\sqrt{1-\frac{9}{25}}=\sqrt{\frac{16}{25}}=±\frac{4}{5}$
$\mathrm{sin}t=-\frac{4}{5}\phantom{\rule{1em}{0ex}}\left(\because \frac{3\pi }{2}
$\mathrm{csc}t=\frac{1}{\mathrm{sin}t}=-\frac{5}{4}$
$\mathrm{csc}t=\frac{1}{\mathrm{sin}t}=-\frac{5}{4}$
$\mathrm{cot}t=\frac{-3}{4}$

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