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Usually, Trigonometry is used to deal with right-angled triangles. Trigonometry helps to find out the sides and angles using the relationship between them. Both the Sine and Cosine rules apply to any triangle - not just right-angled triangles.


LabellingEdit

Triangle

A labled triangle

  • In right angled triangles, the side next to the angle you are using is called the 'adjacent', the side opposite, is called that. The longest side is called the hypotenuse.
  • For the sine rule, the cosine rule and areas of triangles, the sides are labelled a,b and c and the angles opposite a,b and c are labelled A, B and C.

SineEdit

$ sin(x)=opposite/hypotenuse $

CosineEdit

$ cos(x)=adjacent/hypotenuse $

TangentEdit

$ tan(x)=opposite/adjacent $

Memory AidsEdit

The sine, cosine, and tangents can be remembered by this rhyme: Some old hag came and had tea one afternoon (sine: opposite/hypotenuse, cosine: adjacent/hypotenuse, tangent: opposite/adjacent).

Another good memory aid is SOH, CAH, TOA. They are abbreviations for [sine=opposite/hypotenuse], [cos=adjacent/hypotenuse] and [tan=opposite/adjacent].

The Sine RuleEdit

Sine equation

The Cosine RuleEdit

$ a^2=b^2 + c^2 -2bccos(A) $