Question

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

Answer 1

Given $\cos \theta =4/5$

$=\frac{adjacentside}{hypotenuse}$

Let the opposite 'n'

from Pythagoras theorem

$(AC{)}^r=(AB{)}^r+(BC{)}^r$ $AB=x$

$5^r=x^r+4^r$ $BC=4$

$x^r=5^r-4^r$ $AC=5$

$x^r=5^r-4^r$

$x^r=25-16=9$

$x=\sqrt{9}\Rightarrow x=3$

Then $\sin =\frac{oppositeside}{hypoteuse}=\frac{3}{5}$

$\tan \theta =\frac{oppositeside}{adjacentside}\frac{3}{4}$

$\sec \theta =\frac{hypotenuse}{adjacentside}=\frac{1}{\cos \theta }=\frac{5}{4}$

$cosec\theta =\frac{hypotenuse}{adjacentside}=\frac{1}{\sin \theta }=\frac{5}{3}$