Lösung 4.3:3c
Aus Online Mathematik Brückenkurs 1
(Unterschied zwischen Versionen)
K (Robot: Automated text replacement (-{{Displayed math +{{Abgesetzte Formel)) |
K (hat „Solution 4.3:3c“ nach „Lösung 4.3:3c“ verschoben: Robot: moved page) |
Version vom 15:03, 22. Okt. 2008
With the help of the Pythagorean identity, we can express \displaystyle \cos v in terms of \displaystyle \sin v,
| \displaystyle \cos^2 v + \sin^2 v = 1\qquad\Leftrightarrow\qquad \cos v = \pm\sqrt{1-\sin^2 v}\,\textrm{.} |
In addition, we know that the angle \displaystyle v lies between \displaystyle -\pi/2 and \displaystyle \pi/2, i.e. either in the first or fourth quadrant, where angles always have a positive x-coordinate (cosine value); thus, we can conclude that
| \displaystyle \cos v = \sqrt{1-\sin^2 v} = \sqrt{1-a^2}\,\textrm{.} |
