Processing Math: Done
Solution 4.4:2f
From Förberedande kurs i matematik 1
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| - | { | + | Using the unit circle shows that the equation <math>\cos 3x = -1/\!\sqrt{2}</math> |
| - | < | + | has two solutions for <math>0\le 3x\le 2\pi\,</math>, |
| - | {{ | + | |
| + | {{Displayed math||<math>3x = \frac{\pi}{2} + \frac{\pi}{4} = \frac{3\pi}{4}\qquad\text{and}\qquad 3x = \pi + \frac{\pi}{4} = \frac{5\pi}{4}\,\textrm{.}</math>}} | ||
[[Image:4_4_2_f.gif|center]] | [[Image:4_4_2_f.gif|center]] | ||
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| + | We obtain the other solutions by adding multiples of <math>2\pi</math>, | ||
| + | |||
| + | {{Displayed math||<math>3x = \frac{3\pi}{4} + 2n\pi\qquad\text{and}\qquad 3x = \frac{5\pi}{4} + 2n\pi\,,</math>}} | ||
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| + | i.e. | ||
| + | |||
| + | {{Displayed math||<math>x = \frac{\pi}{4} + \frac{2}{3}n\pi\qquad\text{and}\qquad x = \frac{5\pi}{12} + \frac{2}{3}n\pi\,,</math>}} | ||
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| + | where ''n'' is an arbitrary integer. | ||
Current revision
Using the unit circle shows that the equation 
2 
3x2
| 2+4=43and3x=+4=45. |
We obtain the other solutions by adding multiples of
+2nand3x=45+2n |
i.e.
| 4+32nandx=125+32n |
where n is an arbitrary integer.
