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


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


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