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# Find the Value of the Other Five Trigonometric Functions Sin X = 3 5 , X in Quadrant I - Mathematics

Find the value of the other five trigonometric functions
$\sin x = \frac{3}{5},$ x in quadrant I

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#### Solution

We have:
$\sin x = \frac{3}{5}\text{ and x are in the first quadrant.}$
$\text{ In the first quadrant, all six T - ratios are positive .}$
$\therefore \cos x = \sqrt{1 - \sin^2 x} = \sqrt{1 - \left( \frac{3}{5} \right)^2} = \frac{4}{5}$
$\tan x = \frac{\sin x}{\cos x} = \frac{\frac{3}{5}}{\frac{4}{5}} = \frac{3}{4}$
$\cot x = \frac{1}{\tan x} = \frac{1}{\frac{3}{4}} = \frac{4}{3}$
$\sec x = \frac{1}{\cos x} = \frac{1}{\frac{4}{5}} = \frac{5}{4}$
$cosec x = \frac{1}{\sin x} = \frac{1}{\frac{3}{5}} = \frac{5}{3}$

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#### APPEARS IN

RD Sharma Class 11 Mathematics Textbook
Chapter 5 Trigonometric Functions
Exercise 5.2 | Q 1.4 | Page 25
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