Find sin 2theta if theta is in the first quadrant and tan theta = 40/9 ??

1 Answer
Jul 18, 2018

720/16817201681.

Explanation:

Using the Identity, sin2theta=(2tantheta)/(1+tan^2theta)sin2θ=2tanθ1+tan2θ, we get,

sin2theta=(2*40/9)/{1+(40/9)^2}sin2θ=24091+(409)2,

=80/9-:1681/81=809÷168181.

rArr sin2theta=720/1681sin2θ=7201681.

theta in Q_1 rArr 0 lt theta lt pi/2 rArr 0 lt 2theta lt piθQ10<θ<π20<2θ<π.

:. sin2theta gt 0.