PrepZii

mixed

Sine, Cosine and Projection Formulae

The source begins with standard triangle notation: sides $a,b,c$ opposite angles $A,B,C$ .

Sine rule

\frac{a}{\sin A}=\frac{b}{\sin B}=\frac{c}{\sin C}

Cosine formula

\cos A=\frac{b^2+c^2-a^2}{2bc},\quad \cos B=\frac{c^2+a^2-b^2}{2ca},\quad \cos C=\frac{a^2+b^2-c^2}{2ab}

Projection formula

a=b\cos C+c\cos B,\quad b=c\cos A+a\cos C,\quad c=a\cos B+b\cos A

$a$

side length or set/cardinality symbol from context

$b$

side length or constant from context

$c$

side length or constant from context

$A$

angle, event, or set from context

$B$

angle, event, or set from context

$C$

angle, event, or set from context