Trig Question...Help Please!!!

sin( 2A )  =  2 sin( A ) cos( A )

 

We can find   sin( A )   using the Pythagorean identity.

 

sin² A  +  cos² A   =   1

sin² A  +  (-4/5)²   =   1

sin² A  +  (16/25)  =   1

sin² A   =   1 - 16/25

sin² A   =   9/25                     Take the square root of both sides.

sin A = 3/5                             Since sin is positive in Quadrant II, we only take the positive root.

 

Now we can find   sin( 2A )   using the double-angle identity.

 

sin( 2A )  =  2 sin( A ) cos( A )

sin( 2A )  =  2 (3/5) (-4/5)

sin( 2A )  =  -24/25