Question

Find the exact value of cos 157.5°.

Answer 1

Cos 157.5º=-cos (180º-157.5º)=-cos 22.5=-cos(45/2)

cos Ф/2=⁺₋√((1+cosФ)/2).

In this case 157.5º is in the second quadrant, therefore we use the following equation:
cos Ф/2=-√((1+cosФ)/2).          (we will have a negative number)

cos 157.5º=-cos (45/2)=-√((1+cos 45º)/2)
=-√((1+√2/2)/2)
=-√((2+√2)/4)
=-√(2+√2) / 2   (≈-0.92387...)

Answer: cos 157.5º= -√(2+√2) / 2