| pi | ||
obliczyc wartosci funkcji trygonometrycznych kąta | . | |
| n |
| an | pi | |||
wpisanego w kolo o promieniu R=1 to | bedzie linia sinusa kąta | a apotema | ||
| 2 | n |
| an2 | ||
ln=√1− | bedzie linia cosinusa | |
| 4 |
| pi | an | pi | an2 | |||||
Wiec sin | = | cos | =√1− | |||||
| n | 2 | n | 4 |
| pi | ||
cos36= | ||
| 5 |
| 5−√5 | 1 | 3+√5 | ||||
wiec dla n=5 a5= √ | i l5= | √ | ||||
| 2 | 2 | 2 |
| √5+1 | ||
to cos 36= | ||
| 4 |
| pi | ||
Natomiast cos72=sin18 =sin | ||
| 10 |
| √5−1 | 1 | 5+√5 | ||||
dla n=10 a10= | i l10= | √ | to wedlug wzoru | |||
| 2 | 2 | 2 |
| pi | √5−1 | |||
sin | =sin18= | |||
| 10 | 4 |
| √5+1 | √5−1 | 2√5 | √5 | |||||
wobec tego cos36+cos72= | + | = | = | |||||
| 4 | 4 | 4 | 2 |
