Answer:
To find the exact value of the cosine of 135 degrees, we can use the fact that the cosine of an angle is equal to the negative of the sine of that angle's supplement. The supplement of 135 degrees is 45 degrees, and the sine of 45 degrees is 0.7071067811865476 (or 1/sqrt(2)). Therefore, the cosine of 135 degrees is equal to the negative of 0.7071067811865476, or -0.7071067811865476.
The angle 135 degrees is in the third quadrant, where the sine and cosine are both negative.
The angle with the horizontal for an angle of 135 degrees is 45 degrees.