Processing Math: Done
Solution 4.4:3d
From Förberedande kurs i matematik 1
(Difference between revisions)
m (Lösning 4.4:3d moved to Solution 4.4:3d: Robot: moved page) |
m |
||
| (One intermediate revision not shown.) | |||
| Line 1: | Line 1: | ||
| - | {{ | + | First, we observe from the unit circle that the equation has two solutions for <math>0^{\circ}\le 3x\le 360^{\circ}\,</math>, |
| - | < | + | |
| - | + | {{Displayed math||<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]] | ||
| + | |||
| + | This means that all of the equation's solutions are | ||
| + | |||
| + | {{Displayed math||<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. | ||
| + | |||
| + | {{Displayed math||<math>x = 5^{\circ} + n\cdot 120^{\circ}\qquad\text{and}\qquad x = 55^{\circ} + n\cdot 120^{\circ}\,\textrm{.}</math>}} | ||
Current revision
First, we observe from the unit circle that the equation has two solutions for 
3x360
| and3x=180−15=165. |
This means that all of the equation's solutions are
+n 360and3x=165+n360 |
for all integers n, i.e.
| +n120andx=55+n120. |
