# 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:

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

## Author: mathtuition88

http://mathtuition88.com

## One thought on “sin(180-x)”

1. Reblogged this on Singapore Maths Tuition and commented:

I realize that many students from top IP schools don’t know these formula! (Not entirely their fault since the teachers don’t teach/emphasize it.)
Nevertheless, they are often tested in the harder A Math Trigonometry questions, it is a must to know if you are aiming for A1.

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