assume the angle is in the first quadrant, and sin theta equals 1/5. what is sin 2 theta?

Answer 1

sin(theta)=1/5

cos(theta)=sqroot[1-sin(teta)^2]

cos(theta)=sqroot[1-(1/5)^2]

cos(theta)=sqroot(1-1/25)

cos(theta)=sqroot(25/25-1/25)

cos(theta)=sqroot(24/25)

cos(theta)=sqroot(6*4/25)

cos(theta)=sqroot(6*2^2/5^2)

cos(theta)=(2/5)*sqroot(6)

sin(2theta)=2*sin(theta)*cos(theta)

sin(2theta)=2*(1/5)*(2/5)sqroot(6)

sin(2theta)=(4/25)*sqroot(6)