Question #e3313

Question

1334 views around the world

You can reuse this answer
Creative Commons License

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:

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