sin(180-x)

I realize that many students from top IP schools don’t know these formula. In fact many students have not even seen or heard of these formula in school! (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.

  • Negative Angles Formula
  • Supplementary Angles Formula
  • Complementary Angles Formula

Click on the link “View Original Post” below to see the original post with the formulae.

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Negative angles:

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

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

Supplementary angles:

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

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

Complementary angles:

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

Reason: right angled triangle 90-x

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

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Author: mathtuition88

https://mathtuition88.com/

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