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

$approx 0.26$

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