Find the exact value of cos 157.5°.

1 answer:

3 0

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

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