# Math Help - trig help explanation

1. ## 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

2. 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.