Trigonometry/Plane

Template:TOCright 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

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

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