Revision sheet · Mathematics

Trigonometric functions

Degrees to radians: $R = \frac{π}{180} D$
Arc length with the angle in radians: $l = r θ$
sin(A + B): $sin (A + B) = sin A cos B + cos A sin B$
sin(A − B): $sin (A - B) = sin A cos B - cos A sin B$
cos(A + B): $cos (A + B) = cos A cos B - sin A sin B$
cos(A − B): $cos (A - B) = cos A cos B + sin A sin B$
tan(A + B): $tan (A + B) = \frac{t a n A + t a n B}{1 - t a n A t a n B}$
tan(A − B): $tan (A - B) = \frac{t a n A - t a n B}{1 + t a n A t a n B}$
sin 2A: $sin 2 A = 2 sin A cos A$
cos 2A: $cos 2 A = cos^{2} A - sin^{2} A$
tan 2A: $tan 2 A = \frac{2 t a n A}{1 - t a n ^{2} A}$
sin 3A: $sin 3 A = 3 sin A - 4 sin^{3} A$
cos 3A: $cos 3 A = 4 cos^{3} A - 3 cos A$
cos x + cos y: $cos x + cos y = 2 cos \frac{x + y}{2} cos \frac{x - y}{2}$
cos x − cos y: $cos x - cos y = - 2 sin \frac{x + y}{2} sin \frac{x - y}{2}$
sin x + sin y: $sin x + sin y = 2 sin \frac{x + y}{2} cos \frac{x - y}{2}$
sin x − sin y: $sin x - sin y = 2 cos \frac{x + y}{2} sin \frac{x - y}{2}$
2 sin x cos y: $2 sin x cos y = sin (x + y) + sin (x - y)$
2 cos x cos y: $2 cos x cos y = cos (x + y) + cos (x - y)$
2 sin x sin y: $2 sin x sin y = cos (x - y) - cos (x + y)$
cos²A from cos 2A: $cos^{2} A = \frac{1 + c o s 2 A}{2}$
sin²A from cos 2A: $sin^{2} A = \frac{1 - c o s 2 A}{2}$
tan 3A: $tan 3 A = \frac{3 t a n A - t a n ^{3} A}{1 - 3 t a n ^{2} A}$