Question

Assume that θ is a positive acute angle. Given:cosθ= 17/8 ​ Find: sin2θ

Answer 1

We can start by using the Pythagorean identity: sin²θ + cos²θ = 1

Since we know cosθ, we can solve for sinθ:

sin²θ + (17/8)² = 1
sin²θ = 1 - (289/64)
sin²θ = 175/64
sinθ = √(175/64)

Now, we can use the double angle formula for sine:

sin2θ = 2sinθcosθ
sin2θ = 2(√(175/64))(17/8)
sin2θ = (17/8)√(175/16)
sin2θ = (17/8)(5/2) (since √(175/16) = 5/2)
sin2θ = 85/32

Therefore, sin2θ = 85/32.