sin(180-x)

Trigonometry Identities

Negative angles:

$\sin (-x)=-\sin x$
$\boxed{\cos (-x)=\cos x}$ (Still Positive!)
$\tan (-x)=-\tan x$

Reason: $-x$ is in the “C” quadrant so Cosine is still positive.

Supplementary angles:

$\boxed{\sin (180^\circ -x)=\sin x}$ (Still positive!)
$\cos (180^\circ -x)=-\cos x$
$\tan (180^\circ -x)=-\tan x$

Reason: $180^\circ -x$ is in the “S” quadrant so Sine is still positive.

Complementary angles:

$\sin (90^\circ -x)=\cos x$
$\cos (90^\circ -x)=\sin x$
$\tan (90^\circ -x)=\cot x$

Reason:

$\sin (90^\circ -x)=\cos x=a/c$
$\cos (90^\circ -x)=\sin x=b/c$
$\tan (90^\circ -x)=\cot x=a/b$