Given that sin Ø = 0.3251 and Ø is in quadrant​ I, find sin 2Ø

Question

I have been having trouble finding a way to solve sin 2Ø when  sin Ø is a decimal and I'm not sure what steps to take to find the end result. Am I over thinking it?

Answer 1

sinθ = 0.3251

 

Since cos²θ + sin²θ = 1, cos²θ = 1 - sin²θ

 

                                     cosθ = √(1 - sin²θ) = 0.9457

 

So, sin(2θ) = 2sinθcosθ = 0.6149