Trigonometric ratios of angle A in terms of cosec 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 sin A in terms of cosec A

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

Value of Cos A in terms of cosec A

From Trigonometric Identity

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

Value of tan A in terms of cosec A

Now Value of tan is given by

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

Value of sec A in terms of cosec A

$sec A = \frac {1}{cos A} = \frac {cosec A}{ \sqrt {cosec^2 A -1}}$

Value of cot A in terms of cosec A

$\cot A = \frac {1}{\tan A} =\sqrt {cosec^2 A -1}$

In Short