Formulas for goniometric functions
Kapitoly: Basic goniometric functions, The unit circle, Cyclometric Arcus functions, Sine, cosine, tangent and cotangent, Formulas for goniometric functions, Graphs of goniometric functions, The sine and cosine theorem
Formulas for working with goniometric functions. The formulas in abbreviated form can be downloaded in PDF format.
Basic formulas
$$\begin{eqnarray} \sin^2(x)+\cos^2(x)&=&1\\ \tan(x)\cdot\cot(x)&=&1\\ \sin(x)&=&\cos(x-\frac{\pi}{2})\\ \cos(x)&=&\sin(x+\frac{\pi}{2})\\ \cot(x)&=&\tan(-x+\frac{\pi}{2}) \end{eqnarray}$$
Expression of tangent and cotangent
$$\begin{eqnarray} \tan(x)&=&\frac{\sin(x)}{\cos(x)}\\ \cot(x)&=&\frac{\cos(x)}{\sin(x)} \end{eqnarray}$$
Functions with argument 2x and x/2
$$\begin{eqnarray} \sin(2x)&=&2\sin(x)\cos(x)\\ \cos(2x)&=&\cos^2(x)-\sin^2(x)\\ \left|\sin(\frac{x}{2})\right|&=&\sqrt{\frac{1-\cos(x)}{2}}\\ \left|\cos(\frac{x}{2})\right|&=&\sqrt{\frac{1+\cos(x)}{2}} \end{eqnarray}$$
Summation formulas
$$\begin{eqnarray} \sin(x+y)&=&\sin(x)\cos(y)+\cos(x)\sin(y)\\ \sin(x-y)&=&\sin(x)\cos(y)-\cos(x)\sin(y)\\ \cos(x+y)&=&\cos(x)\cos(y)-\sin(x)\sin(y)\\ \cos(x-y)&=&\cos(x)\cos(y)+\sin(x)\sin(y)\\ \end{eqnarray}$$