Question

If sin theta=3/5 then cos theta where theta is in first quadrant.

Answer 1

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Answer 2

Answer:

$\cos\theta=\frac{4}{5}$

Step-by-step explanation:

Given : $\sin\theta=\frac{3}{5}$

To find : The value of $\cos\theta$ where $\theta$ is in first quadrant ?

Solution :

$\sin\theta=\frac{3}{5}$

Applying trigonometric identity,

$\sin^2\theta+\cos^2\theta=1$

$(\frac{3}{5})^2+\cos^2\theta=1$

$\frac{9}{25}+\cos^2\theta=1$

$\cos^2\theta=1-\frac{9}{25}$

$\cos^2\theta=\frac{25-9}{25}$

$\cos^2\theta=\frac{16}{25}$

$\cos\theta=\frac{4}{5},-\frac{4}{5}$

In first quadrant $\cos\theta$ is always positive.

Therefore, $\cos\theta=\frac{4}{5}$