If sin(x)=-4/5 and (x) is in Quadrant III, find tan(x/2)

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- Nov 10th 2012, 10:57 AMderek1008Can anyone help me with this problem?
If sin(x)=-4/5 and (x) is in Quadrant III, find tan(x/2)

- Nov 10th 2012, 11:39 AMskeeterRe: Can anyone help me with this problem?
if $\displaystyle x$ is a quad III angle ...

(1) by sketching a reference triangle in quad III, you can calculate the value of $\displaystyle \cos{x}$.

(2) $\displaystyle \pi < x < \frac{3\pi}{2} \implies \frac{\pi}{2} < \frac{x}{2} < \frac{3\pi}{4}$

... which says $\displaystyle \frac{x}{2}$ is a quad II angle. Therefore, $\displaystyle \tan\left(\frac{x}{2}\right) < 0$.

now use your half angle identity for tangent.