Pythagoras' Theorem & Trigonometry

Pythagoras' Theorem

$a^2+b^2=c^2$

TOA

$\tan\theta=\dfrac{\text{O}}{\text{A}}$

CAH

$\cos\theta=\dfrac{\text{A}}{\text{H}}$

SOH

$\sin\theta=\dfrac{\text{O}}{\text{H}}$

Only for right-angled triangles

$\sin(180^\circ-\theta)=\sin\theta$

$\cos(180^\circ-\theta)=-\cos\theta$

Sine Rule

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

Cosine Rule

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

Area of Triangle

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

3-digit angle measured clockwise from North, e.g. $081^\circ$