Trigonometric Identities and matrix operations

Rotation matrix :

R = [{cos θ , -sin θ},
         {sinθ , cosθ}]

{X1, Y1} = R x {X0, Y0}
       

Pythagoras theorem:

sin^2 θ + cos^2 θ = 1

1 + cot^2 θ = cosec^2 θ = 1/sin^2θ

tan^2 θ + 1 = sec^2 θ = 1/cos^2θ

Odd and even properties

cos(−x) = cos(x),  sin(−x) = − sin(x),  tan(−x) = − tan(x)

Compound Angle Formula:

cos(A + B) = cos A cos B − sin A sin B
cos(A − B) = cos A cos B + sin A sin B
sin(A + B) = sin A cos B + cos A sin B
sin(A − B) = sin A cos B − cos A sin B
tan(A + B) = (tan A + tan B) / (1 − tan A tan B)
tan(A − B) = (tan A − tan B) / (1 + tan A tan B)

cos 2θ = cos^2 θ − sin^2 θ = 2 cos^2 θ − 1 = 1 − 2 sin^2 θ
 sin 2θ = 2 sin θ cos θ
tan 2θ = 2 tan θ / (1 − tan^2 θ)