How do you evaluate cos[(pi/2)/2]?

2 Answers
SCooke
Mar 14, 2018

Evaluate the parenthetical expression first, then the cosine follows.
cos (pi/4) = 0.707

Explanation:

The cosine function just applies to whatever is defined to it. It may be a function itself. In this case it is just and expression.

(pi/2)/2 = pi/4

cos (pi/4) = 0.707 (assuming radian measures)

Aviv S.
Mar 16, 2018

The answer is sqrt2/2.

Explanation:

The previous answer is the most correct way to compute this, but I would also like to point out that it is also possible to use the half-angle theorem in this case:

cos(theta/2)=sqrt((1+costheta)/2)

In this case, our theta is pi/2:

color(white)=cos((pi/2)/2)

=sqrt((1+cos(pi/2))/2)

=sqrt((1+0)/2)

=sqrt((1)/2)

=sqrt1/sqrt2

=1/sqrt2

=1/sqrt2color(red)(*sqrt2/sqrt2)

=sqrt2/sqrt2^2

=sqrt2/2~~0.707107...

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