if cos theta = the square root of 3 over 2, find csc theta

Question

Please help me find csc theta if cos theta = the square root of 3 over 2

Answer 1

Since cos(θ) = adjacent/hypotenuse then we can draw a triangle like this:

and use the Pythagorean Theorem to solve for y.

(√3)² + y² = 2²

3 + y² = 4

y² = 4 - 3

y² = 1

y = 1

Then we can use the ratio csc(θ) = hypotenuse/opposite and get csc(θ) = 2/1 = 2

Answer 2

Use identify sin(theta)^2 + cos(theta)^2 = 1, to find sin(theta).

csc(theta) = 1/sin(theta).