Given cotθ = 9/40 in quadrant 3, determine cscθ

Answer 1

If in quadrant 3, then csc θ will be negative.

cot θ = x/y = 9/40. x = -9, y = -40

Hypotenuse, h = √(x²+y²) = √1681 = 41

csc θ = h/y = -41/40

Answer 2

Cotangent is the ratio of the adjacent side to the opposite side of the triangle in question, so the adjacent side is -9 and the opposite side is -40 in the third quadrant,

The Csc is the ratio of the hypotenuse to the opposite side of the triangle.

The hypotenuse is √ ( -9² + -40²) = 41, so the Csc is 41 / -40 .