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:

\[\sin x = \frac{3}{5}\text{ and x are in the first quadrant.}\]

\[\text{ In the first quadrant, all six T - ratios are positive .}\]

\[\therefore \cos x = \sqrt{1 - \sin^2 x} = \sqrt{1 - \left( \frac{3}{5} \right)^2} = \frac{4}{5}\]

\[\tan x = \frac{\sin x}{\cos x} = \frac{\frac{3}{5}}{\frac{4}{5}} = \frac{3}{4}\]

\[\cot x = \frac{1}{\tan x} = \frac{1}{\frac{3}{4}} = \frac{4}{3}\]

\[\sec x = \frac{1}{\cos x} = \frac{1}{\frac{4}{5}} = \frac{5}{4}\]

\[cosec x = \frac{1}{\sin x} = \frac{1}{\frac{3}{5}} = \frac{5}{3}\]

Concept: Signs of Trigonometric Functions

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