Trigonometry

Right Angle Triangle

 

$$sin(θ) = {opp}/{hyp}$$
$$cos(θ) = {adj}/{hyp}$$
$$tan(θ) = {opp}/{adj}$$

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

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