Question

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

Answer 1

`720/1681`.

Explanation:

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

`sin2theta=(2*40/9)/{1+(40/9)^2}`,

`=80/9-:1681/81`.

`rArr sin2theta=720/1681`.

`theta in Q_1 rArr 0 lt theta lt pi/2 rArr 0 lt 2theta lt pi`.

`:. sin2theta gt 0`.