The exact value of cos 135° is -√2 / 2.
To understand why this is the case, we can break it down. The angle 135° is located in the second quadrant of the unit circle. In this quadrant, cosine values are negative.
We can also relate it to its reference angle. The reference angle for 135° is 180° – 135° = 45°. The cosine of 45° is √2 / 2. Since we are in the second quadrant where the cosine is negative, we take the negative value: -√2 / 2.
So, the exact value of cos 135° is indeed -√2 / 2.