Question

If sin θ = $-\frac{1}{3}$ and θ does not lie in the third quadrant, find the values ofa. cos θb. cot θ

Answer 1

sinθ = -1/3 , where θ doesn't lie in the 3rd quadrant. it means θ lies in 1st, 2nd , or 4th quadrants. but sine is negative in 3rd and 4th quadrant. so, here we will consider 4th quadrant.

in 4th quadrant , cosine and secant be positive.

now, sinθ = -1/3 = p/h
p = 1 and h = 3
then, b = √(h² - p²) = √(3² - 1²) = 2√2
now, cosθ = b/h = 2√2/3

and cotθ = b/p = 2√2/1 = 2√2
but θ lies in 4th quadrant so, cotθ = -2√2


hence, cosθ = 2√2/3

cotθ = -2√2