Given $tantheta=-3/4$ and $pi/2<theta<pi$ , how do you find $tan(theta/2)$ ?

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Given $tantheta=-3/4$ and $pi/2<theta<pi$ , how do you find $tan(theta/2)$ ?

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Answer 1 · 2016-11-07T13:10:38

The answer is $=tan(theta/2)=3$

Explanation:

You can use the formula $tan2theta=(2tantheta)/(1-tan^2theta)$

$:. tantheta=(2tan(theta/2))/(1-tan^2(theta/2))$
Let $tan(theta/2)=t$
then $-3/4=(2t)/(1-t^2)$
$-3+3t^2=8t$
$3t^2-8t-3=0$
This is a quadratic equation
$Delta=64+36=100$
So, $t=(8+-sqrt100)/6=8+-10$

$t=3$ or $t=-1/3$

We keep only $t=3$ as $pi/2< theta < pi$

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Given $tantheta=-3/4$ and $pi/2<theta<pi$ , how do you find $tan(theta/2)$ ?

1 Answer

Explanation:

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Humanities

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Given tantheta=-3/4tantheta=-3/4 and pi/2<theta<pipi/2<theta<pi, how do you find tan(theta/2)tan(theta/2)?

1 Answer

Explanation:

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Given $tantheta=-3/4$ and $pi/2<theta<pi$ , how do you find $tan(theta/2)$ ?