Processing Math: Done
To print higher-resolution math symbols, click the
Hi-Res Fonts for Printing button on the jsMath control panel.
jsMath

Lösung 4.4:2d

Aus Online Mathematik Brückenkurs 1

(Unterschied zwischen Versionen)
Wechseln zu: Navigation, Suche
K (Robot: Automated text replacement (-{{Displayed math +{{Abgesetzte Formel))
K (hat „Solution 4.4:2d“ nach „Lösung 4.4:2d“ verschoben: Robot: moved page)

Version vom 15:13, 22. Okt. 2008

Apart from the fact that there is a 5x, this is a normal trigonometric equation of the type siny=a. If we are only interested in solutions which satisfy 05x2, then a sketch of the unit circle shows that there are two such solutions, 5x=4 and the reflectionally symmetric solution 5x=−4=34.

All of the equation's solutions are obtained from all values of 5x which differ by a multiple of 2 from either of these two solutions,

5x=4+2nand5x=43+2n

where n is an arbitrary integer.

If we divide both of these by 5, we obtain the solutions expressed in terms of x alone,

x=20+52nandx=203+52n

where n is an arbitrary integer.

Von „http://wiki.sommarmatte.se/wikis/2009/bridgecourse1-TU-Berlin/index.php/L%C3%B6sung_4.4:2d“