Pythagoras’ Theorem & Trigonometry
Pythagoras' theorem
$a^2+b^2=c^2$
Trigonometric ratios
$\tan\theta=\frac{\text{opposite}}{\text{adjacent}}$
$\cos\theta=\frac{\text{adjacent}}{\text{hypotenuse}}$
$\sin\theta=\frac{\text{opposite}}{\text{hypotenuse}}$
$\cos\theta=\frac{\text{adjacent}}{\text{hypotenuse}}$
$\sin\theta=\frac{\text{opposite}}{\text{hypotenuse}}$
TOA CAH SOH is applicable for only right-angled triangles
Obtuse angles
$\sin(180^\circ-\theta)=\sin\theta$
$\cos(180^\circ-\theta)=-\cos\theta$
$\cos(180^\circ-\theta)=-\cos\theta$
Sine rule
$\dfrac{a}{\sin A}=\dfrac{b}{\sin B}$
Cosine rule
$c^2=a^2+b^2-2 ab \cos C$
Area of triangle
$\text{Area of triangle}=\frac{1}{2}ab \sin C$
Bearings
A bearing is a 3-digit positive number with units of degree to show direction clockwise from the north direction.
