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Revision:Sine and Cosine Formulae

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TSR Wiki > Study Help > Subjects and Revision > Revision Notes > Mathematics > Sine and Cosine Formulae

Contents

Sine and Cosine Formulae

\displaystyle \sin x = \sin (180 - x)

e.g. \displaystyle \sin 130 = \sin (180 - 130) = \sin 50


\displaystyle \cos x = -\cos (180 - x)


The Sine Rule

This works in any triangle:

\displaystyle \frac{a}{\sin A} = \frac{b}{\sin B} = \frac{c}{\sin C}


alternatively:

\displaystyle \frac{\sin A}{a} = \frac{\sin B}{b} = \frac{\sin C}{c}


NOTE: the triangle is labelled as follows:



(diagram of the labelled triangle is missing)



The Cosine Rule

\displaystyle c^2 = a^2 + b^2 - 2ab\cos C


can also be written as:

\displaystyle a^2 = b^2 + c^2 - 2bc\cos A


This also works in any triangle.


The area of a triangle

This works out the area of any triangle.

\displaystyle \mathsf{Area} = \frac{1}{2} ab\sin C

(using the above notation)


This formula is useful if you don't know the height of a triangle (since you need to know the height for the \frac{1}{2}\mathsf{base}\times\mathsf{height} formula).

Comments

Thia article is missing diagrams.

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