Draw a unit circle (centre 0,0 on a number plane with radius 1).
Now draw 2 diagonal lines through the centre ( should look like y=x and y=-x ).
The angles these lines make with the x axis are called the related angle. The top right quadrant is the first, followed by the top left, then bottom left, and finally the bottom right being the 4th quadrant.
You should have 4 related angles, each in a different quadrant. Draw perpendicular lines straight down from the intersection of your diagonal lines and the unit circle, this will make 4 congruent right angled triangles. Let the angle made at the origin of the triangle be theta.
Now you can use sin/cos/tan to prove a few indentities for theta in each of the 4 different quadrants. Hint: Let the hypotenuse be 'r' as it is the radius of the unit circle, and then let the vertical side of the triangle be 'y' and the horizontal side be 'x'.
You will come up with a general case for sin, cos, and tan in each quadrant which you can use for any length 'r'. However since it's a unit circle and the radius is 1, let r=1 and see what happens to these identities. These new identities are special cases on a unit circle.
Using this diagram you can also derive other identities, so just play around with it a bit (see when sin/cos/tan are positive or negative).
You can also see things such as sin@ = cos(90-@) through the diagram.
Note: I did this instead of just telling you the identities as you will understand it more if you derive it yourself instead of accepting it as fact.
