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Solution 4.4:3d

From Förberedande kurs i matematik 1

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m (Lösning 4.4:3d moved to Solution 4.4:3d: Robot: moved page)
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First, we observe from the unit circle that the equation has two solutions for
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<center> [[Image:4_4_3d.gif]] </center>
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<math>0^{\circ }\le \text{3}x\le \text{36}0^{\circ }</math>,
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<math>3x=15^{\circ }</math>
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and
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<math>3x=180^{\circ }-15^{\circ }=165^{\circ }</math>
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[[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
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<math>3x=15^{\circ }+n\centerdot 360^{\circ }</math>
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and
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<math>3x=165^{\circ }+n\centerdot 360^{\circ }</math>
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for all integers
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<math>n</math>, i.e.
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<math>x=5^{\circ }+n\centerdot 120^{\circ }</math>
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and
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<math>x=55^{\circ }+n\centerdot 120^{\circ }</math>

Revision as of 09:57, 1 October 2008

First, we observe from the unit circle that the equation has two solutions for 03x360,


3x=15 and 3x=180−15=165


This means that all of the equation's solutions are


3x=15+n360 and 3x=165+n360


for all integers n, i.e.


x=5+n120 and x=55+n120

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