cos(φ) = xp , sin(φ) = yp , tan(φ) = yp xp sin2 (x) + cos2 (x) = 1 and cos−2 (x) = 1 + tan2 (x). cos(a ± b) = cos(a) cos(b) ∓ sin(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) sin(p) + sin(q) = 2 sin( 12 (p + q)) cos( 12 (p − q)) sin(p) − sin(q) = 2 cos( 21 (p + q)) sin( 12 (p − q)) cos(p) + cos(q) = 2 cos( 12 (p + q)) cos( 12 (p − q)) cos(p) − cos(q) = −2 sin( 21 (p + q)) sin( 21 (p − q)) 2 cos2 (x) = 1 + cos(2x) sin(π − x) = sin(x) sin( 12 π − x) = cos(x) sin(x) = sin(a) cos(x) = cos(a) ⇒ ⇒ tan(x) = tan(a) ⇒ arctan(x) = arcsin √ 2 sin2 (x) = 1 − cos(2x) cos(π − x) = − cos(x) cos( 12 π − x) = sin(x) , , , x = a ± 2kπ or x = (π − a) ± 2kπ, k ∈ IN x = a ± 2kπ or x = −a ± 2kπ π x = a ± kπ and x = 6 ± kπ 2 x x2 + 1 = arccos √ 1 x2 + 1 , sin(arccos(x)) = p 1 − x2