How do I remember the common values of cosx, sinx and tanx?

To remeber the equations us SOH CAH TOA. This is Sinx = Opposite/Hypotenuse, Cos x = Adjacent/Hypotenuse and Tanx = Opposite/Adjacent. For values x=pi/3 and x=pi/6 always start by drawing an equilateral of side length 1. You know that each of the angles must be 60 degrees, or pi/3. Remeber radians are degrees * 2pi/360. Then draw a straight line down the top to bisect the bottom side. This gives a right angled triangle with the other angles being pi/3 and pi/6. We know that the bottom side must be half of what it was before so it's 1/2. The hypotenuse of the triangle remains 1 and we can use pythagoras to calculate the final side. So

>(1)^2 = ((1/2)^2 +h^2) 
>1=1/4 +h^2
>3/4=h^2
>h=3^(1/2)/2

Finally using SOH CAH TOA you can calculate the values by reading off of the diagram.

Similarly a right angled isoceles triangle can be used to calculate values where x = pi/4.

(Best explained with a diagram)