# Math Help - unit circle help

1. ## unit circle help

hi, i need a little bit of help with questions such as:

use a unit circle diagram to find all angles between 0deg and 360deg:

sine 0.5

cos 1/root2

etc...

i can usually do this as i have a summary of angles of :
multiples of
90deg
45deg
30deg

i know what the x and y values are from these.. but when i find the angles i get confused on what angle sine is .. eg with root3/2 i dont know if the angle going anti clockwise is 30 or 60 unless i use my calculator..

i hope you guys understand what im talking about... as my teacher keeps mentioning the acute angle which i have no idea on where is is ??

2. Acute means an angle less than 90 degrees.

The instructions say to use your unit circle diagram... do you have one?

3. Yes i do have one, but just for test purposes i cant bring one in....
also i know what acute means but im just wondering where its measured from..

thanks anyway

4. Originally Posted by whitestrat
Yes i do have one, but just for test purposes i cant bring one in....
also i know what acute means but im just wondering where its measured from..

thanks anyway
All angles are measured from the positive x-axis in a counterclockwise fashion.

Reference angles are measured from either the positive or negative x-axis and are measured in either a clockwise or countclockwise fashion. You can tell if you need to go clockwise or counterclockwise by looking to see what quadrant the angle needs to fall into.

For example:
$sin(\theta) = -\frac{\sqrt{3}}{2}$

$sin(\theta)$ is the y-coordinate on the unit circle and is negative, so your angle must lie in either the third or fourth quadrants. The reference angle will be an acute angle such that
$sin(\theta) = \left | - \frac{\sqrt{3}}{2} \right | = \frac{\sqrt{3}}{2}$

So the reference angle is $60^o$. Since this needs to be in QIII or QIV we get two angles for $\theta$:
$\theta = 180^o + 60^o = 240^o$
and
$\theta = 360^o - 60^o = 300^o$

-Dan