# Trigonometry/Plane

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Plane trigonometry involves solving the mathematics of triangles. The law of sines and cosines are fundamental to this.

## Law of sines

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

## Area of a triangle

 ${\displaystyle {\text{Area}}={\frac {1}{2}}bc\sin A}$ ${\displaystyle {\text{Area}}={\frac {1}{2}}ab\sin C}$ ${\displaystyle {\text{Area}}={\frac {1}{2}}ac\sin B}$

## Law of cosines

This law uses the Pythagorean theorem, but this includes non-right angles.
 ${\displaystyle a^{2}=b^{2}+c^{2}-2ab\cos A}$ ${\displaystyle b^{2}=a^{2}+c^{2}-2ab\cos B}$ ${\displaystyle c^{2}=b^{2}+a^{2}-2ab\cos C}$

## Heron's area formula

s is the semi-perimeter
 ${\displaystyle s={\frac {1}{2}}(a+b+c)}$ ${\displaystyle {\text{Area}}={\sqrt {s(s-a)(s-b)(s-c)}}}$

## References

1. Trigonometry (7th ed.), Addison Wesley, 2001, 0-321-05759-7
2. "Trigonometry". Britannica 28: 619. (1993). University of Chicago. 0-85229-571-5.