A neat trig trick

It's useful to be able to remember the values of sin, cos and tan for commonly-encountered angles. Here is a handy method to help you reconstruct them if you forget:

Radians Degrees sin cos tan

0 0 √0/2=0 √4/2=1 0

π/6 30 √1/2=1/2 √3/2 1/√3

π/4 45 √2/2=1/√2 √2/2=1/√2 1

π/3 60 √3/2 √1/2=1/2 √3

π/2 90 √4/2=1 √0/2=0 ∞

Notice the patterns here: the sin values are in the sequence √n/2, n=0,1,2,3,4, and the cos values go the other way, because cos(x) = sin(π/2-x). And tan(x)=sin(x)/cos(x). So all you really need to remember is how to construct the "sin" column.

Be aware, though, that there is no deep magic going on here, because the angles in the table do not go up in a neat linear sequence. For them to do that, you'd have to add in 15 degrees (π/12) and 75 degrees (5π/12). The expressions for those are not nice (they involve square roots inside square roots) and you won't need their exact values for A level, so I've left them out.