How do you evaluate cos [(pi)/4]?

1 Answer
Daniel L.
Dec 4, 2015

cos (pi/4)=sqrt(2)/2 see explanation for details.

Explanation:

Angle pi/4 rad or 45^@ can be an angle in isosceles right triangle, so its catheti are equal and its hypothenuse is sqrt(2) times longer. For example if the catheti are 1 unit long, then the hypothenuse is sqrt(2) units.

Sine is a quotient of the cathetus opposite to the angle and the hypothenuse, so:

sin 45^@=1/sqrt(2)=sqrt(2)/2

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