Trigonometric ratios of angle A in terms of cos A

In this post ,we will see how we can write all the Trigonometric ratios of angle A in the terms of cos A. Here we would be focusing on acute angle A only

Value of sin A in terms of sin A

From Trigonometric Identity

$\sin ^2 A + \cos ^2 A= 1$
or
$\sin ^2 A = 1- \cos ^2 A$
$\sin A = \sqrt { 1 – \cos ^2 A}$

Value of tan A in terms of cos A

Now Value of tan is given by

$tan A = \frac { \sin A}{\cos A} = \frac { \sqrt { 1 – \cos ^2 A}}{\cos A}}$

Value of cosec A in terms of cos A

Now Value of cosec is given by

$\csc A = \frac {1}{\sin A} = \frac {1}{\sqrt { 1 – \cos ^2 A}} $

Value of sec A in terms of cos A

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

Value of cot A in terms of cos A

$\cot A = \frac {1}{\tan A} = \frac {\cos A}{ \sqrt { 1 – \cos ^2 A}}$

In Short