Question

use reference angles to find the exact value. rationalize the denominator of your answer, if needed. select \undefined\ if applicable. cos 225° =

Explanation:

Step1: Find the reference angle

The angle \(225^{\circ}\) is in the third - quadrant. The reference angle \(\theta_{r}=225^{\circ}-180^{\circ} = 45^{\circ}\).

Step2: Determine the sign of cosine

In the third - quadrant, cosine is negative. And we know that \(\cos45^{\circ}=\frac{\sqrt{2}}{2}\). So \(\cos225^{\circ}=-\cos45^{\circ}\).

Step3: Get the exact value

\(\cos225^{\circ}=-\frac{\sqrt{2}}{2}\)

Answer:

\(-\frac{\sqrt{2}}{2}\)