Question

If cos $cos\theta =\frac{7}{25}$, find the values of all T-ratios of $\theta$

Answer 1

$cos\theta =\frac{7}{25}$
Therefore,
Base = 7cm
Hypotenuse = 25cm

By Pythagoras Theorem,
$h^2=p^2+b^2$
$p^2=h^2-b^2$
$p^2={25}^2-7^2=625-49$
$p=\sqrt{576}=24cm$

Perpendicular = 24cm

$sin\theta =\frac{p}{h}=\frac{24}{25}$

$cos\theta =\frac{7}{25}$ [given]

$tan\theta =\frac{p}{b}=\frac{24}{7}$

$cosec\theta =\frac{25}{24}\left[\frac{1}{sin\theta }\right]$

$sec\theta =\frac{25}{7}\left[\frac{1}{cos\theta }\right]$

$cot\theta =\frac{7}{24}\left[\frac{1}{tan\theta }\right]$