Question

Need Help! : If A is an obtuse angle in a triangle and sin A is 5/13, calculate the exact value of sin 2A

Answer 1

as A is obtuse, we know that 2A will lie in the 3rd or 4th quadrants and therefore sin 2A will be negative.

Now sin 2A = 2 sin A cos A

As sin^2 A + cos^2 A = 1, cos A = +-sqrt(1 - sin^2 A)

In this case we know we want the negative root. So now

sin 2A = - 2 sin A sqrt(1 - sin^2 A)

Now substitute and evaluate.