Processing Math: Done
To print higher-resolution math symbols, click the
Hi-Res Fonts for Printing button on the jsMath control panel.
jsMath

Solution 4.4:2e

From Förberedande kurs i matematik 1

(Difference between revisions)
Jump to: navigation, search
m (Lösning 4.4:2e moved to Solution 4.4:2e: Robot: moved page)
Line 1: Line 1:
-
{{NAVCONTENT_START}}
+
This is almost the same equation as in exercise d. First, we determine the solutions to the equation
-
<center> [[Image:4_4_2e.gif]] </center>
+
when
-
{{NAVCONTENT_STOP}}
+
<math>0\le \text{5}x\le \text{2}\pi </math>, and using the unit circle shows that there are two of these:
 +
<math>\text{5}x\text{ }=\frac{\pi }{6}</math>
 +
and
 +
<math>\text{5}x\text{ }=\pi -\frac{\pi }{6}=\frac{5\pi }{6}</math>.
 +
 
[[Image:4_4_2_e.gif|center]]
[[Image:4_4_2_e.gif|center]]
 +
 +
We obtain the remaining solutions by adding multiples of
 +
<math>2\pi </math>
 +
to the two solutions above:
 +
 +
 +
<math>\text{5}x\text{ }=\frac{\pi }{6}+2n\pi </math>
 +
and
 +
<math>\text{5}x\text{ }=\frac{5\pi }{6}+2n\pi </math>
 +
(
 +
<math>n</math>
 +
an arbitrary integer),
 +
 +
or if we divide by
 +
<math>\text{5}</math>:
 +
 +
 +
<math>x\text{ }=\frac{\pi }{30}+\frac{2}{5}n\pi </math>
 +
and
 +
<math>x\text{ }=\frac{\pi }{6}+\frac{2}{5}n\pi </math>
 +
(
 +
<math>n</math>
 +
an arbitrary integer).

Revision as of 08:36, 1 October 2008

This is almost the same equation as in exercise d. First, we determine the solutions to the equation when 05x2, and using the unit circle shows that there are two of these: 5x =6 and 5x =−6=65.


We obtain the remaining solutions by adding multiples of 2 to the two solutions above:


5x =6+2n and 5x =65+2n ( n an arbitrary integer),

or if we divide by 5:


x =30+52n and x =6+52n ( n an arbitrary integer).

Retrieved from "http://wiki.math.se/wikis/2008/bridgecourse1-ImperialCollege/index.php/Solution_4.4:2e"