How do you evaluate #sin (pi/4) cos (pi/6) - sin (pi/6) cos (pi/4)#?

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Answer 1 · 2016-04-05T13:29:51

#0.26#

The most straightforward way to do it (in my opinion) is to substitute #pi = 180^o# and use degrees.

Therefore,

#sin(pi/4) = sin(45) = sqrt2/2#
#cos(pi/6) = cos(30) = sqrt3/2#
#sin(pi/6) = sin(30) = 1/2#
#cos(pi/4) = cos(45) = sqrt2/2#

Put these into the original equation, and you get

#sqrt2/2*sqrt3/2 - 1/2*sqrt2/2#

Rearranging these become

#sqrt2/2((sqrt3-1)/2) = (sqrt6-sqrt2)/4#

If you want this in a decimal form, use a calculator or a savant

#approx 0.26#