If sin theta =20/29 and theta is actute, find the values of sin2 theta

Question

Solve without using tables

Answer 1

Use the identity sin(2θ) = 2sin(θ)cos(θ)

You have sin(θ) = 20/29

Given that θ is acute (meaning it's in the first quadrant), and, the opposite side is 20 and the hypotenuse is 29, you can calculate the adjacent side with the Pythagorean Theorem as 21. That means the cos(θ) = 21/29.

So sin(2θ) = 2(20/29)(21/29) = 840/841