Question

Please help!

Given that sine(theta)=5/8 and the angle theta is in quadrant 1, find the value for the cosine of theta.

Answer 1

Answer: A

Explanation:

sin∅ = ⅝ in the first quadrant means you have a triangle with a point at the origin with (opposite side / hypothenuse) = ⅝. This means it is 5 units tall and its diagonal side is 8 units long. Using the Pythagorean theorem, if the width of the triangle is x, x²+5²=8², so x²+25=64. This means x²=64-25=39 and x=+√39. Cos∅ would equal the ratio of your adjacent side (width) to your hypothenuse length, so it would be √39 / 8, which is answer choice A.

Answer 2

A) cos θ = sqrt(39) / 8

Explanation:

sin^2 θ + cos^2 θ = 1

(5/8)^2 + cos^2 θ = 1

25/64 + cos^2 θ = 1

cos^2 θ = 64/64 - 25/64

cos^2 θ = 39/64

cos θ = sqrt(39) / 8

since the angle is in the first quadrant, cos is positive.

hope this helps! <3