If $sintheta=-1/3$ and $pi<theta<(3pi)/2$ , how do you find $tan (theta/2)$ ?

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Answer 1 · 2016-06-26T05:25:11

. $-3-2sqrt 2$

$theta$ is in the 3rd quadrant, So, $tan theta > 0$ ..

Also, $theta/2$ is in the 2nd and, therefore, $tan (theta/2) <0$ .

Use $sin theta =-1/3= (2 tan (theta/2))/(1+tan^2(theta/2))$

Solving for negative root, $tan (theta/2)=-3-2sqrt 2$ .

If sintheta=-1/3sintheta=-1/3 and pi<theta<(3pi)/2pi<theta<(3pi)/2, how do you find tan (theta/2)tan (theta/2)?