To find the exact value of cos 132°, we can use the cosine angle subtraction formula and reference angles.
First, note that 132° lies in the second quadrant, where the cosine function is negative. The reference angle for 132° is calculated by subtracting it from 180°:
Reference angle = 180° – 132° = 48°.
Now, we can write:
cos 132° = -cos 48°.
While we can find cos 48° using a calculator or trigonometric tables, its exact value in terms of radicals isn’t straightforward. However, we can express it in terms of known values.
For practical scenarios, you could find an approximate value using a calculator:
cos 132° ≈ -0.6691.
So, the exact value of cos 132° in the context of its reference angle is:
cos 132° = -cos 48°.