1.2. Trigonometry

Pythagorean indentity:

(1.5)\[\sin^2 x+\cos^2 x=1\]

Sine and cosine additive identities

(1.6)\[\sin(x+y)=\sin x\cos y+\cos x\sin y\]

(1.7)\[\cos(x+y)=\cos x\cos y-\sin x\sin y\]

Double angle formulas:

(1.8)\[\sin(2x)=2\sin x\cos x\]

(1.9)\[\cos(2x)=\cos^2 x-\sin^2 x=2cos^2 x-1=1-2\sin^2x\]

Half angle formulas:

(1.10)\[\sin(\frac{x}{2})=\pm \sqrt{\frac{1-\cos x}{2}}\]

(1.11)\[\cos(\frac{x}{2})=\pm \sqrt{\frac{1+\cos x}{2}}\]

You can read more about trigonometry in Adams and Essex [AE18], chapter P.6.