Trigonometric ratios of angle A in terms of sin A

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

Value of Cos A in terms of sin A

From Trigonometric Identity

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

Value of tan A in terms of sin A

Now Value of tan is given by

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

Value of cosec A in terms of sin A

Now Value of cosec is given by

$\csc A = \frac {1}{\sin A} $

Value of sec A in terms of sin A

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

Value of cot A in terms of sin A

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

In Short