If sinu= (-5/7) and pie<u< (3pie/2) find sin 2u

Answer 1

Calculate sin(2u) using the identity:
sin(2x)=2sin(x)cos(x) ....(1)

From "pie<u< (3pie/2)"
we conclude that u is in the third quadrant where sin(u)<0 and cos(u)<0.

From sin(u)=(-5/7), calculate cos(u) using cos²(u)+sin²(u)=1.

Make sure the value of both sin(u) and cos(u) are negative and substitute in equation (1) above.