sin(180-x)

Trigonometry Identities

all science teachers crazy maths tuition

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: right angled triangle 90-x

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