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
