Lösung 4.4:3d
Aus Online Mathematik Brückenkurs 1
(Unterschied zwischen Versionen)
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First, we observe from the unit circle that the equation has two solutions for <math>0^{\circ}\le 3x\le 360^{\circ}\,</math>, | First, we observe from the unit circle that the equation has two solutions for <math>0^{\circ}\le 3x\le 360^{\circ}\,</math>, | ||
| - | {{ | + | {{Abgesetzte Formel||<math>3x = 15^{\circ}\qquad\text{and}\qquad 3x = 180^{\circ} - 15^{\circ} = 165^{\circ}\,\textrm{.}</math>}} |
[[Image:4_4_3_d.gif|center]] | [[Image:4_4_3_d.gif|center]] | ||
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This means that all of the equation's solutions are | This means that all of the equation's solutions are | ||
| - | {{ | + | {{Abgesetzte Formel||<math>3x = 15^{\circ} + n\cdot 360^{\circ}\qquad\text{and}\qquad 3x = 165^{\circ} + n\cdot 360^{\circ}\,,</math>}} |
for all integers ''n'', i.e. | for all integers ''n'', i.e. | ||
| - | {{ | + | {{Abgesetzte Formel||<math>x = 5^{\circ} + n\cdot 120^{\circ}\qquad\text{and}\qquad x = 55^{\circ} + n\cdot 120^{\circ}\,\textrm{.}</math>}} |
Version vom 08:59, 22. Okt. 2008
First, we observe from the unit circle that the equation has two solutions for \displaystyle 0^{\circ}\le 3x\le 360^{\circ}\,,
| \displaystyle 3x = 15^{\circ}\qquad\text{and}\qquad 3x = 180^{\circ} - 15^{\circ} = 165^{\circ}\,\textrm{.} |
This means that all of the equation's solutions are
| \displaystyle 3x = 15^{\circ} + n\cdot 360^{\circ}\qquad\text{and}\qquad 3x = 165^{\circ} + n\cdot 360^{\circ}\,, |
for all integers n, i.e.
| \displaystyle x = 5^{\circ} + n\cdot 120^{\circ}\qquad\text{and}\qquad x = 55^{\circ} + n\cdot 120^{\circ}\,\textrm{.} |
