All important Trigonometric ratios and series formulae

This page provides the most important formulae for trigonometric ratios and their series.
These formulae are aimed for secondary as well as high school students. Some of them are advanced, so if you think they are not in your class, you can skip those.

Expansions of some trigonometric ratios

$e^x=1+x+\frac{x^2}{2!}+\frac{x^3}{3!}+\frac{x^4}{4!}+.....\mathrm{\infty }$

$\sin (x)=x-\frac{x^3}{3!}+\frac{x^5}{5!}-\frac{x^7}{7!}+.....\mathrm{\infty }$

$\cos (x)=1-\frac{x^2}{2!}+\frac{x^4}{4!}-\frac{x^6}{6!}+.....\mathrm{\infty }$

$\tan (x)=x+\frac{1}{3}{x}^3+\frac{2}{15}{x}^5+\frac{17}{315}{x}^7.....\mathrm{\infty }$

Trigonometric Series

$\cos (\alpha )+\cos (\alpha +\beta )+\cos (\alpha +2\beta )+\cos (\alpha +3\beta )+.....+\cos (\alpha +(n-1)\beta )=\frac{\sin (\frac{n\beta }{2})\cos (2\alpha +(n-1)\frac{\beta }{2})}{\sin (\frac{\beta }{2})}$

$\sin (\alpha )+\sin (\alpha +\beta )+\sin (\alpha +2\beta )+\sin (\alpha +3\beta )+.....+\sin (\alpha +(n-1)\beta )=\frac{\sin (\frac{n\beta }{2})\sin (2\alpha +(n-1)\frac{\beta }{2})}{\sin (\frac{\beta }{2})}$

Hope you are helped with it.