Question

If the angle tita is in the third quadrant and cot tita=3, then the value of sin is​

Answer 1

Given

Angle theta is in 3rd quadrant.

and cot theta = 3 .

Sin theta we have to find.

Solution

We know that

1+ cosec²theta = cot²theta .

$\csc( \theta) = \sqrt{ \cot {}^{2} ( \theta) - 1}$

$\csc( \theta) = \sqrt{9 - 1}$

Cosec theta = √8

cosec theta. = 2√2

we know that sin is reciprocal of cosec so,

sin theta = 1/2√2

as theta lies in 3rd quadrant where sin functions-ve ,So

Sin theta = -1/2√2