If cos u = 30/34 find sin 2u

Answer 1

cosine is positive in quadrants 1 and 4

for quadrant 1:

adjacent=30 and hypotenuse = 34

then by pythagorean, the opposite is sqrt( 34*34 - 30*30)

= sqrt( 256) = 16

then the sine is 16/34 = 8/17 while the cosine is 30/34 = 15/17.

sin 2u = 2 sin u cos u = 2(8/17)(15/17) = 240/289

for quadrant 4:

the sine shall be -8/17 which forces sin 2u to be -240/289