Trigonometry/Plane

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

Law of sines

${\frac {a}{\sin A}}={\frac {b}{\sin B}}$

${\frac {a}{\sin A}}={\frac {c}{\sin C}}$

${\frac {b}{\sin B}}={\frac {c}{\sin C}}$

Area of a triangle

${\text{Area}}={\frac {1}{2}}bc\sin A$

${\text{Area}}={\frac {1}{2}}ab\sin C$

${\text{Area}}={\frac {1}{2}}ac\sin B$

Law of cosines

This law uses the Pythagorean theorem, but this includes non-right angles.

$a^{2}=b^{2}+c^{2}-2ab\cos A$

$b^{2}=a^{2}+c^{2}-2ab\cos B$

$c^{2}=b^{2}+a^{2}-2ab\cos C$

Heron's area formula

s is the semi-perimeter

$s={\frac {1}{2}}(a+b+c)$

${\text{Area}}={\sqrt {s(s-a)(s-b)(s-c)}}$