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
A Level Maths Notes: C3 Using the Multiple Angle Formulae To Find Values of Trigonometric 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 find
and
for
example if we choose the values of
and
properly.
To find
we
can choose
and
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 of
is
