The article deals with the importance of the use of basic figures in mathematics. As an example the derivation of a new rule is demonstrated, by which series of cosnx and sinnx may be evolved without having to refer to a book. The starting formulae for n = 2 and n = 3 can immediately be read from adequate figures, being found by a simple reasoning. The series of higher integer values of n can be found afterwards by using the right half of Pascal's triangle. For proving this rule the complex forms of sine and cosine are needed. These formulae can be found easily from basic figures, constructed in the unit circle in the complex plane, depending on Euler's theorem. This theorem is proved by means of Maclaurin's series evolution, the starting point of which is also directly readable from a simple figure. The aim of the article is to point out a way of quickly deriving formulae, which are not inherently easy to memorize.