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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