Trigonometry

Right Angle Triangle

\$\$sin(θ) = {opp}/{hyp}\$\$

Any Triangle

Law of Sines

\$\${sin(A)}/a = {sin(B)}/b = {sin(C)}/c\$\$

Law of Cosines

\$\$a^2 = b^2+c^2-bc{cos(A)}\$\$
\$\$b^2 = a^2+c^2-ac{cos(B)}\$\$
\$\$c^2 = a^2+b^2-ab{cos(C)}\$\$

Identities

\$\$sin^2(θ)+cos^2(θ) = 1\$\$
\$\$sec(θ) = 1/{cos(θ)}\$\$
\$\$cosec(θ) = 1/{sin(θ)}\$\$
\$\$tan(θ) = {sin(θ)}/{cos(θ)}\$\$
\$\$cot(θ) = {cos(θ)}/{sin(θ)}\$\$
\$\$1+tan^2(θ) = sec^2(θ)\$\$
\$\$1+cot^2(θ) = cosec^2θ\$\$
\$\$sin(-θ) = -sin(θ)\$\$
\$\$cos(-θ) = cos(θ)\$\$
\$\$tan(-θ) = -tan(θ)\$\$
\$\$cosec(-θ) = -cosec(θ)\$\$
\$\$sec(-θ) = sec(θ)\$\$
\$\$cot(-θ) = -cot(θ)\$\$
\$\$sin(a±b) = sin(a)cos(b)±sin(b)cos(a)\$\$
\$\$cos(a±b) = cos(a)cos(b)±sin(a)sin(b)\$\$
\$\$tan(a±b) = {tan(a)±tan(b)}/{1±tan(a)tan(b)}\$\$
\$\$sin(2θ) = 2sin(θ)cos(θ)\$\$
\$\$cos(2θ) = cos^2θ-sin^2θ\$\$
\$\$cos(2θ) = 1-2sin^2(θ)\$\$
\$\$cos(2θ) = 2cos^2(θ)-1\$\$
\$\$tan(2θ) = {2tan(θ)}/{1-tan^2(θ)}\$\$
\$\$sin^2(θ) = {1-cos(2θ)}/2\$\$
\$\$cos^2(θ) = {1+cos(2θ)}/2\$\$