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Thread: trig ratios

  1. #1
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    trig ratios

    write each of the following as the ratios of positive acute angles.

    in the examples i understand that $\displaystyle sin 330 = -sin 30$

    but can someone please explain to me how it is that

    $\displaystyle cos (3/4) \pi $= $\displaystyle -cos (1/4) \pi$

    and $\displaystyle sin -(4/5) \pi $= $\displaystyle -sin (1/5) \pi$

    i understand that $\displaystyle \pi$ = 180 but i am not geting it when i express each of the sectors in terms of $\displaystyle \pi$
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  2. #2
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    Quote Originally Posted by sigma1 View Post
    write each of the following as the ratios of positive acute angles.

    in the examples i understand that $\displaystyle sin 330 = -sin 30$

    but can someone please explain to me how it is that

    $\displaystyle cos (3/4) \pi $= $\displaystyle -cos (1/4) \pi$

    and $\displaystyle sin -(4/5) \pi $= $\displaystyle -sin (1/5) \pi$

    i understand that $\displaystyle \pi$ = 180 but i am not geting it when i express each of the sectors in terms of $\displaystyle \pi$
    Hi sigma1,

    $\displaystyle \cos \frac{3 \pi}{4}$ is a QII angle. Related angle is $\displaystyle \pi - \frac{3 \pi}{4}=\frac{\pi}{4}$.
    Cosine is negative in the second quadrant.

    $\displaystyle \cos \frac{\pi}{4}$ is a QI angle. Cosine is positive in the first quadrant.

    Therefore, $\displaystyle \cos \frac{3 \pi}{4}=-\cos \frac{\pi}{4}$

    The sin function is an odd function, meaning $\displaystyle \sin (-\theta)=-\sin \theta$

    $\displaystyle \sin -\frac{4 \pi}{5}=-\sin \frac{4\pi}{5}$

    Related angle is $\displaystyle \pi-\frac{4\pi}{5}=\frac{\pi}{5}$

    $\displaystyle \sin \frac{4\pi}{5}$ is a QII angle. Sin is positive in the first and second quadrants.

    Therefore, $\displaystyle \sin -\frac{4\pi}{5}=-\sin \frac{\pi}{5}$
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