Question

Trigonometry
Trigonometric Functions
Given: Cos θ = (3/5), Find: Csc θ

Answer 1

csc theta = 5/4

Explanation:

cos theta = 3/5

cos theta = adjacent side/ hypotenuse

Let adjacent side = 3 and the hypotenuse = 5

csc theta = hypotenuse/ opposite side

We need to find the opposite side

We know that this is a right triangle, so we can use the Pythagorean theorem

(adj)^2 + (opp)^2 = (hyp)^2

3^2 + (opp)^2 = 5^2

9+ (opp)^2 = 25

Subtract 9 from each side

9-9+ (opp)^2 = 25-9

(opp)^2 = 16

Take the square root of each side

sqrt( (opp)^2) = sqrt(16)

opp = 4

csc theta = hypotenuse/ opposite side = 5/4