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Andreas345
- Grothendieck
- Innlegg: 828
- Registrert: 13/10-2007 00:33
[tex]sin(\frac{45}{2})=\sqrt{\frac{1-cos(2\cdot \frac{45^{\circ}}{2})}{2}}[/tex]
[tex]sin(\frac{45}{2})=\sqrt{\frac{1-cos(45^{\circ})}{2}}[/tex]
[tex]cos(45^{\circ})[/tex] er en eksakt trigonometrisk verdi som vi vet er
[tex]cos(45^{\circ})=\frac{\sqrt{2}}{2}[/tex]
[tex]sin(22.5)=\sqrt{\frac{1-\frac{\sqrt{2}}{2}}{2}}=\sqrt{\frac{1-\frac{\sqrt{2}}{2}}{2}\cdot \frac{2}{2}}=\sqrt{\frac{2-\sqrt{2}}{4}}=\frac{sqrt{2-\sqrt{2}}}{2}[/tex]
[tex]sin(\frac{45}{2})=\sqrt{\frac{1-cos(45^{\circ})}{2}}[/tex]
[tex]cos(45^{\circ})[/tex] er en eksakt trigonometrisk verdi som vi vet er
[tex]cos(45^{\circ})=\frac{\sqrt{2}}{2}[/tex]
[tex]sin(22.5)=\sqrt{\frac{1-\frac{\sqrt{2}}{2}}{2}}=\sqrt{\frac{1-\frac{\sqrt{2}}{2}}{2}\cdot \frac{2}{2}}=\sqrt{\frac{2-\sqrt{2}}{4}}=\frac{sqrt{2-\sqrt{2}}}{2}[/tex]
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Andreas345
- Grothendieck
- Innlegg: 828
- Registrert: 13/10-2007 00:33
?? Bare delte helt på slutten, for å bekrefte at [tex]sin(\frac{45}{2})=sin(22.5)[/tex]