Calculus Question

Question

If cos θ = 3/5, and sin θ > 0, find sin θ

a. 4/5

b. -4/5

c. 5/3

d. -5/3

Answer 1

Use the Pythagorean identity

sin²(x) + cos²(x) = 1

Answer 2

Answer is a. 4/5

sin²(θ) + cos²(θ) = 1, so knowing the value of cos(θ) tells us ±sin(θ) = ±√1-cos²(θ) = ±√1 - 9/25 = ±√16/25

We're also told sin(θ) is positive so we can drop the ±, and we end up with √16/25 = 4/5