Doble vinkler 2.8
Posted: 25/06-2008 18:47
Jeg skal finne [tex]sin\ \frac{\pi}{8}[/tex] .
Bruker formelen;
[tex]sin v= \pm \frac{1}{\sqrt2} \cdot \sqrt{1-sin2v}[/tex]
setter inn ;
[tex]sin\ \frac{\pi}{8} =\pm \frac{1}{\sqrt2} \cdot \sqrt{1-sin2 \cdot \frac{\pi}{8}}[/tex]
[tex]sin\ \frac{\pi}{8}=\pm \frac{1}{\sqrt2} \cdot \sqrt{1-sin\ \frac{\pi}{4}}[/tex]
[tex]sin\ \frac{\p}{8}=\pm \frac{\sqrt{1-sin\ \frac{\pi}{4}}}{\sqrt2}[/tex]
Eksakt sin verdi for vinkel 45 grader med radianen [tex]\frac{\pi}{4}=\frac{\sqrt2}{2}[/tex]
Dermed;
[tex]sin\ \frac{\pi}{8}=\pm \frac{\sqrt{1-\frac{\sqrt2}{2}}}{\sqrt2}[/tex]
[tex]sin^2\ \frac{\pi}{8}=({1-\frac{\sqrt2}{2}})\cdot \frac {1}{2}[/tex]
[tex]sin^2\ \frac{\pi}{8}=\frac{2-\sqrt2}{4}[/tex]
[tex]sin\ \frac{\pi}{8}=\pm \sqrt{\frac{2-\sqrt2}{4}[/tex]
Vinkelen ligger i 1.kvadrant, dermed positiv da;
[tex]sin\ \frac{\pi}{8}=\frac{\sqrt{2-\sqrt2}}{2}[/tex]
Har jeg gjort noen feil her?
Bruker formelen;
[tex]sin v= \pm \frac{1}{\sqrt2} \cdot \sqrt{1-sin2v}[/tex]
setter inn ;
[tex]sin\ \frac{\pi}{8} =\pm \frac{1}{\sqrt2} \cdot \sqrt{1-sin2 \cdot \frac{\pi}{8}}[/tex]
[tex]sin\ \frac{\pi}{8}=\pm \frac{1}{\sqrt2} \cdot \sqrt{1-sin\ \frac{\pi}{4}}[/tex]
[tex]sin\ \frac{\p}{8}=\pm \frac{\sqrt{1-sin\ \frac{\pi}{4}}}{\sqrt2}[/tex]
Eksakt sin verdi for vinkel 45 grader med radianen [tex]\frac{\pi}{4}=\frac{\sqrt2}{2}[/tex]
Dermed;
[tex]sin\ \frac{\pi}{8}=\pm \frac{\sqrt{1-\frac{\sqrt2}{2}}}{\sqrt2}[/tex]
[tex]sin^2\ \frac{\pi}{8}=({1-\frac{\sqrt2}{2}})\cdot \frac {1}{2}[/tex]
[tex]sin^2\ \frac{\pi}{8}=\frac{2-\sqrt2}{4}[/tex]
[tex]sin\ \frac{\pi}{8}=\pm \sqrt{\frac{2-\sqrt2}{4}[/tex]
Vinkelen ligger i 1.kvadrant, dermed positiv da;
[tex]sin\ \frac{\pi}{8}=\frac{\sqrt{2-\sqrt2}}{2}[/tex]
Har jeg gjort noen feil her?
