If $ \cos \theta=\frac{4}{5} $, find all other trigonometric ratios of angle $ \theta $

Given:

\( cos \theta=\frac{4}{5} \)

To do:

We have to find all other trigonometric ratios of angle \( \theta \).

Solution:  

We know that,

$\sin ^{2} \theta+\cos ^{2} \theta=1$

$ \tan \theta=\frac{\sin \theta}{\cos \theta}$

Therefore,

$\sin \theta=\sqrt{1-\cos ^{2} \theta}$

$=\sqrt{1-(\frac{4}{5})^{2}}$

$=\sqrt{1-\frac{16}{25}}$

$=\sqrt{\frac{25-16}{25}}$

$=\sqrt{\frac{9}{25}}$

$=\frac{3}{5}$
$\tan \theta=\frac{\frac{3}{5}}{\frac{4}{5}}$

$=\frac{3}{5} \times \frac{5}{4}$

$=\frac{3}{4}$

$\cot \theta=\frac{1}{\tan \theta}$

$=\frac{1}{\frac{3}{4}}$

$=\frac{4}{3}$ 

$\operatorname{cosec} \theta=\frac{1}{\sin \theta}$

$=\frac{1}{\frac{3}{5}}$

$=\frac{5}{3}$

$\sec \theta=\frac{1}{\cos \theta}$

$=\frac{1}{\frac{4}{5}}$

$=\frac{5}{4}$

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Updated on: 10-Oct-2022

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