Answer
$\cos 225^{\circ}= -\dfrac{\sqrt 2}{2}$
Work Step by Step
The reference angle of an angle $0 \leq \theta \lt 2\pi $ based on its position can be computed by using the following steps:
a) Quadrant- I: $\theta $
b) Quadrant- II: $180^{\circ}-\theta $
c) Quadrant -III: $\theta - 180^o $
d) Quadrant -IV: $360^{\circ}-\theta $
We can see that the angle $225^{\circ}$ lies in Quadrant III.
Therefore, we have :
Reference angle of $225^{\circ}$ is equal to
$ =225^{\circ}-180^{\circ}=45^{\circ}$
Since, $\cos 45^{\circ}=\dfrac{\sqrt 2}{2}$
So, $\cos 225^{\circ}= -\dfrac{\sqrt 2}{2}$; Because $\theta $ lies in Quadrant-III.
