Suppose that sintheta 35 and theta is in the second quadran

Suppose that sin(theta) = 3/5 and theta is in the second quadrant. Use trigonometric identities to find the following quantities exactly. (a) cos(theta) = (b) sin(2 theta) = (c) cos(2 theta) = (d) tan(2 theta) =

Solution

sin theta=3/5

cos theta=-4/5

sin(2theta)=2sin theta cos theta =2(3/5)(-4/5)=-24/25

cos (2theta) =2cos²theta-1 =2(16/25)-1=7/25

tan (2theta)=sin(2 theta)/cos(2 theta)=-24/7