How do you evaluate $sin((19pi)/12)cos(-pi/6) - cos((19pi)/12)sin(-pi/6)$ ?

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How do you evaluate $sin((19pi)/12)cos(-pi/6) - cos((19pi)/12)sin(-pi/6)$ ?

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Answer 1 · 2016-03-24T22:06:28

I found: $-sqrt(2)/2$

Explanation:

I think we can use the identity:
$sin(x-y)=sin(x)cos(y)-sin(y)cos(x)$
where in our case:
$x=19/12pi$
$y=-pi/6$
so we get:
$sin(19/12pi)cos(-pi/6)-sin(-pi/6)cos(19/12pi)=sin(19/12pi+pi/6)=$
$=sin((19+2)/12pi)=sin(21/12pi)=sin(7/4pi)=-sqrt(2)/2$

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How do you evaluate $sin((19pi)/12)cos(-pi/6) - cos((19pi)/12)sin(-pi/6)$ ?

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How do you evaluate sin((19pi)/12)cos(-pi/6) - cos((19pi)/12)sin(-pi/6)sin((19pi)/12)cos(-pi/6) - cos((19pi)/12)sin(-pi/6)?

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Explanation:

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How do you evaluate $sin((19pi)/12)cos(-pi/6) - cos((19pi)/12)sin(-pi/6)$ ?