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Math Help - 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 sin 330 = -sin 30

    but can someone please explain to me how it is that

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

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

    i understand that \pi = 180 but i am not geting it when i express each of the sectors in terms of \pi
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  2. #2
    A riddle wrapped in an enigma
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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 sin 330 = -sin 30

    but can someone please explain to me how it is that

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

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

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

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

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

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

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

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

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

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

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