Cos(45)= 1/sqrt(2), sin(30)=1/2, you can solve for these values by using properties of 45/45/90 and 30/60/90 triangles, it also helps to remember this- if you go all the way around the unit circle you'll only find 5 values. These values are- 0,1,1/2, sqrt(2)/2, and sqrt(3)/2. If you can remember that cos(x) is always equal to your x value on the units circle and sin(x) is always equal to the Y value on the unit circle, you should be able to derive every other trigonametric ratio. If I know sin(x) and cos(x) at any value of x, I can find tan(x) by dividing sin(x) by cos(x), and in much the same way I can find values for cosecant, secant, and cotangent.
