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Math Help - trig help explanation

  1. #1
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    trig help explanation

    I am sort of getting how to solve trig equations but the part that I am getting confused on is how to find the infinitely other solutions that are written or found in the periodic funtion of that equation. ie ex. sinx = 1/2 but also can be x = pi/6 + 2npi and x=5pi/6 + 2npi.

    I am sure its something I missed but I can't figure it out can someone explain it to me. thanks
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  2. #2
    MHF Contributor
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    Find a picture of a Unit Circle with a few rays marked on it.

    \theta\;=\;0

    \theta\;=\;\frac{\pi}{6}

    \theta\;=\;\frac{\pi}{4}

    \theta\;=\;\frac{\pi}{3}

    \theta\;=\;\frac{\pi}{2}

    \theta\;=\;\frac{2 \pi}{3}

    \theta\;=\;\frac{3 \pi}{4}

    \theta\;=\;\frac{5 \pi}{6}

    \theta\;=\;\pi

    \theta\;=\;\frac{7 \pi}{6}

    \theta\;=\;\frac{5 \pi}{4}

    \theta\;=\;\frac{4 \pi}{3}

    \theta\;=\;\frac{3 \pi}{2}

    \theta\;=\;\frac{5 \pi}{3}

    \theta\;=\;\frac{7 \pi}{4}

    \theta\;=\;\frac{11 \pi}{6}

    Okay, maybe quite a few. It should not be hard to find this picture in your book or maybe here; The Unit Circle

    For \sin(\theta)\;=\;1/2, look really hard at the ray \theta\;=\;\frac{\pi}{6}. Compare it to the ray at \theta\;=\;\frac{5 \pi}{6}. Do they have the same sine (Vertical Component)? Compare \theta\;=\;\frac{\pi}{6} to whatever happens when you go all the way around the circle and end up in the same place. It still has the same properties as \theta\;=\;\frac{\pi}{6}, but we not there any more. We've been around the track once. We are now at \theta\;=\;\frac{\pi}{6}+2\pi.

    Many such explorations could be undertaken. Give it a little thought. It should soak in.
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