TRIG
posted by AL on .
Given that tan¤=3/4 and ¤ is in the second quadrant find sin2¤ (¤=theta)

see other post.

cos theta = + OR  1 / sqrt ( 1 + tan ^ 2 theta )
In Quadrant II, cosine are negative so :
cos theta =  1 / sqrt ( 1 + tan ^ 2 theta )
cos theta =  1 / sqrt [ 1 + ( 3 / 4 ) ^ 2 theta ]
cos theta =  1 / sqrt ( 1 + 9 / 16 )
cos theta =  1 / sqrt ( 16 / 16 + 9 / 16 )
cos theta =  1 / sqrt ( 25 / 16 )
cos theta =  1 / ( 5 / 4 )
cos theta =  4 / 5
sin ^ 2 theta + cos ^ 2 theta = 1
sin ^ 2 theta = 1  cos ^ 2 theta
sin theta = + OR  sqrt ( 1  cos ^ 2 theta )
In Quadrant II, sine are positive so :
sin theta = sqrt ( 1  cos ^ 2 theta )
sin theta = sqrt [ 1  (  4 / 5 ) ^ 2 ]
sin theta = sqrt ( 1  16 / 25 )
sin theta = sqrt ( 25 / 25  16 / 25 )
sin theta = sqrt ( 9 / 25 )
sin theta = 3 / 5
sin 2 theta = 2 sin theta cos theta
sin 2 theta = 2 * 3 / 5 *  4 / 5
sin 2 theta =  24 / 25