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Solution 4.4:3a

From Förberedande kurs i matematik 1

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m (Lösning 4.4:3a moved to Solution 4.4:3a: Robot: moved page)
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The right-hand side of the equation is a constant, so the equation is in fact a normal trigonometric equation of the type
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<center> [[Image:4_4_3a.gif]] </center>
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<math>\text{cos }x=a</math>.
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{{NAVCONTENT_STOP}}
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In this case, we can see directly that one solution is
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<math>x={\pi }/{6}\;</math>. Using the unit circle, it follows that
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<math>x=2\pi -{\pi }/{6}\;={11\pi }/{6}\;</math>
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is the only other solution between
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<math>0</math>
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and
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<math>\text{2}\pi </math>.
[[Image:4_4_3_a.gif|center]]
[[Image:4_4_3_a.gif|center]]
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We obtain all solutions to the equation if we add multiples of
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<math>\text{2}\pi </math>
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to the two solutions above:
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<math>x=\frac{\pi }{6}+2n\pi </math>
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and
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<math>x=\frac{11\pi }{6}+2n\pi </math>
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 +
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where
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<math>n</math>
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is an arbitrary integer.

Revision as of 09:37, 1 October 2008

The right-hand side of the equation is a constant, so the equation is in fact a normal trigonometric equation of the type cos x=a.

In this case, we can see directly that one solution is x=6. Using the unit circle, it follows that x=2−6=116 is the only other solution between 0 and 2.

We obtain all solutions to the equation if we add multiples of 2 to the two solutions above:


x=6+2n and x=611+2n


where n is an arbitrary integer.

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