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Thread: Can anyone help me with this problem?

  1. #1
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    Can anyone help me with this problem?

    If sin(x)=-4/5 and (x) is in Quadrant III, find tan(x/2)
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  2. #2
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    Re: Can anyone help me with this problem?

    Quote Originally Posted by derek1008 View Post
    If sin(x)=-4/5 and (x) is in Quadrant III, find tan(x/2)
    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.
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