Question #e3313

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Answer 1 · 2016-05-06T10:15:04

The value is obtained using the formula for the sine of a difference; it equals #{-\sqrt{3}}/2#, about #-0.866#.

You have the following identities for the sines and cosines of sums and differences:

#\sin(x+y)=\sin(x)\cos(y)+\cos(x)\sin(y)#

#\sin(x-y)=\sin(x)\cos(y)-\cos(x)\sin(y)#

#\cos(x+y)=\cos(x)\cos(y)-\sin(x)\sin(y)#

#\cos(x-y)=\cos(x)\cos(y)+\sin(x)\sin(y)#

Here you have the combination corresponding to the second equation, thus:

#\sin(255°-15°)=\sin(255°)\cos(15°)-\cos(255°)\sin(15°)#

So then we have:

#\sin(255°-15°)=\sin(240°)#
#=\sin(180°+60°)=-\sin(60°)={-\sqrt{3}}/2#