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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