Results 1 to 2 of 2

Thread: trig help explanation

  1. #1
    Aug 2008

    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
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor
    Aug 2007
    Find a picture of a Unit Circle with a few rays marked on it.

    $\displaystyle \theta\;=\;0$

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

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

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

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

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

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

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

    $\displaystyle \theta\;=\;\pi$

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

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

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

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

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

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

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

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

    For $\displaystyle \sin(\theta)\;=\;1/2$, look really hard at the ray $\displaystyle \theta\;=\;\frac{\pi}{6}$. Compare it to the ray at $\displaystyle \theta\;=\;\frac{5 \pi}{6}$. Do they have the same sine (Vertical Component)? Compare $\displaystyle \theta\;=\;\frac{\pi}{6}$ 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 $\displaystyle \theta\;=\;\frac{\pi}{6}$, but we not there any more. We've been around the track once. We are now at $\displaystyle \theta\;=\;\frac{\pi}{6}+2\pi$.

    Many such explorations could be undertaken. Give it a little thought. It should soak in.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. ACF() Explanation
    Posted in the Statistics Forum
    Replies: 0
    Last Post: Jan 18th 2011, 09:24 PM
  2. Need some help and explanation...
    Posted in the Trigonometry Forum
    Replies: 1
    Last Post: Jul 26th 2009, 11:11 AM
  3. I just need an explanation for this please?
    Posted in the Pre-Calculus Forum
    Replies: 4
    Last Post: Jun 8th 2009, 10:59 AM
  4. Explanation Please
    Posted in the Math Topics Forum
    Replies: 1
    Last Post: Apr 1st 2009, 07:59 AM
  5. Explanation
    Posted in the Calculus Forum
    Replies: 4
    Last Post: Aug 27th 2008, 05:24 AM

Search Tags

/mathhelpforum @mathhelpforum