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

Solution 4.4:3c

From Förberedande kurs i matematik 1

(Difference between revisions)
Jump to: navigation, search
m (Lösning 4.4:3c moved to Solution 4.4:3c: Robot: moved page)
Line 1: Line 1:
-
{{NAVCONTENT_START}}
+
If we consider the entire expression
-
<center> [[Image:4_4_3c.gif]] </center>
+
<math>x+\text{4}0^{\circ }</math>
-
{{NAVCONTENT_STOP}}
+
as an unknown, we have a fundamental trigonometric equation and can, with the aid of the unit circle, see that there are two solutions to the equation for
 +
<math>0^{\circ }\le x+\text{4}0^{\circ }\le \text{36}0^{\circ }</math>
 +
namely
 +
<math>x+\text{4}0^{\circ }=\text{65}^{\circ }</math>
 +
and the symmetric solution
 +
<math>x+\text{4}0^{\circ }=\text{18}0^{\circ }-\text{65}^{\circ }=\text{115}^{\circ }</math>.
[[Image:4_4_3_c.gif|center]]
[[Image:4_4_3_c.gif|center]]
 +
 +
It is then easy to set up the general solution by adding multiples of
 +
<math>360^{\circ }</math>,
 +
 +
 +
<math>x+\text{4}0^{\circ }=\text{65}^{\circ }+n\centerdot 360^{\circ }</math>
 +
and
 +
<math>x+\text{4}0^{\circ }=\text{115}^{\circ }+n\centerdot 360^{\circ }</math>
 +
 +
 +
for all integers
 +
<math>n</math>, which gives
 +
 +
 +
<math>x=2\text{5}^{\circ }+n\centerdot 360^{\circ }</math>
 +
and
 +
<math>x=7\text{5}^{\circ }+n\centerdot 360^{\circ }</math>

Revision as of 09:50, 1 October 2008

If we consider the entire expression x+40 as an unknown, we have a fundamental trigonometric equation and can, with the aid of the unit circle, see that there are two solutions to the equation for 0x+40360 namely x+40=65 and the symmetric solution x+40=180−65=115.


It is then easy to set up the general solution by adding multiples of 360,


x+40=65+n360 and x+40=115+n360


for all integers n, which gives


x=25+n360 and x=75+n360

Retrieved from "http://wiki.math.se/wikis/2008/bridgecourse1-ImperialCollege/index.php/Solution_4.4:3c"