# Trigonometry Rules

Sine rule:

$\frac { a }{ sinA } =\frac { b }{ sinB } =\frac { c }{ sinC }$

Other:

$sin\left( -\theta \right) =-sin\theta \\ \\ cos\left( -\theta \right) =cos\theta \\ \\ tan\left( -\theta \right)= -tan\theta$

Important identities:

${ sin }^{ 2 }\theta +{ cos }^{ 2 }\theta =1$

$1+\tan ^{ 2 }{ \theta } =\sec ^{ 2 }{ \theta }$

$1+\cot ^{ 2 }{ \theta } =\csc ^{ 2 }{ \theta }$

Trigonometric fractions:

$\sec ^{ 2 }{ \theta } =\frac { 1 }{ \cos ^{ 2 }{ \theta } } ,\quad \therefore \quad \cos ^{ 2 }{ \theta } =\frac { 1 }{ \sec ^{ 2 }{ \theta } } \\ \\ \csc ^{ 2 }{ \theta } =\frac { 1 }{ \sin ^{ 2 }{ \theta } } ,\quad \therefore \quad \sin ^{ 2 }{ \theta } =\frac { 1 }{ \csc ^{ 2 }{ \theta } } \\ \\ \cot ^{ 2 }{ \theta } =\frac { 1 }{ \tan ^{ 2 }{ \theta } } ,\quad \therefore \quad \tan ^{ 2 }{ \theta } =\frac { 1 }{ \cot ^{ 2 }{ \theta } }$

Area of a triangle:

$\frac { 1 }{ 2 } bcsinA=\frac { 1 }{ 2 } acsinB=\frac { 1 }{ 2 } absinC$

Pythagoras’s Theorem:

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