Question

if sinθ = -1/3 and θ does not lie in third quadrant, find the values of cotθ.​

Answer 1

Answer:

sinθ=− 1/3

=>sin²θ= 1/9

sin²θ+cos² θ=1

1/9+cos²θ=1

cos²θ=1− 1/9

= 9-1/9

=8/9

cosθ=± √8/9

=± 2√2/3

=>cosθ= 2√2/3

orcosθ=−2√2/3

Now sinθ is negative, θ must lie in 3rd or 4th quadrant.

But it is given that θ does not lie in 3rd quadrant..

So θ lies in 4th quadrant

In 4th quadrant cosθ is positive.

=>cosθ=−2√2/3

=>cosθ=2√2/3

Ans= 2√2/3