You can use the unit circle to evaluate your trig functions.  For a given angle, theta, you need to know the corresponding (x, y) coordinate on the unit circle where the terminal ray of the angle intersects the circle.

You can find many points on the unit circle using the info we learned about the 45/45 degree right triangle with hypotenuse 1 and the 30/60 degree right triangle with hypotenuse 1.  Refer to the “The Two Most Important Triangles” movie for a refresher on those triangles.

The 6 trig functions are just the ratios of the 3 sides of any right triangle formed inside the angle

cos(theta) := x/r        sec(theta) := r/x

sin(theta) := y/r        csc(theta) := r/y

tan(theta) := y/x        cot(theta) := x/y

Since these ratios are the same for any chosen radius, the choice of the unit circle (radius = 1) simplifies the ratios (plug in 1 for r everywhere) and the trig functions become

cos(theta) := x        sec(theta) := 1/x

sin(theta) := y         csc(theta) := 1/y

tan(theta) := y/x      cot(theta) := x/y