## Using the Multiple Angle Formulae to Find Values of Triginometric Functions

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