Any A Level student should know the values of any trigonometric function for any angle that is a multiple of 30 or 45 degrees. For convenience they are given below.
0 
30 
45 
60 
90 
120 
135 
150 
180 
210 
225 
240 
270 
300 
315 
330 

0 
0 
1 

1 
0 
1 
0 

0 
1 
1 
0 
1 
1 
Using the values in the above table and the multiple angle formulae
and
We may findandfor example if we choose the values ofandproperly. To findwe can chooseand
Then
Now we follow the normal rules for rationalising the denominator. We multiply numerator and denominator by the conjugate root of the denominator. The conjugate root ofis