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Solution 4.4:8b

From Förberedande kurs i matematik 1

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m (Lösning 4.4:8b moved to Solution 4.4:8b: Robot: moved page)
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Suppose that
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<center> [[Image:4_4_8b.gif]] </center>
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<math>\text{cos }x\ne 0</math>
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, so that we can divide both sides by
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<math>\text{cos }x</math>
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to obtain
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 +
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<math>\frac{\sin x}{\cos x}=\sqrt{3}</math>
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i.e.
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<math>\tan x=\sqrt{3}</math>
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 +
 
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This equation has the solutions
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<math>x=\frac{\pi }{3}+n\pi </math>
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for all integers
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<math>n</math>.
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If, on the other hand,
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<math>\text{cos }x=0</math>, so
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<math>\text{sin }x\text{ }=\pm \text{1}</math>
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( draw a unit circle) and the equation cannot have such a solution.
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Thus, the equation has the solutions
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<math>x=\frac{\pi }{3}+n\pi </math>
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(
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<math>n</math>
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an arbitrary integer).

Revision as of 13:39, 1 October 2008

Suppose that cos x=0 , so that we can divide both sides by cos x to obtain


sinxcosx=3  i.e. tanx=3 


This equation has the solutions x=3+n for all integers n.

If, on the other hand, cos x=0, so sin x =1 ( draw a unit circle) and the equation cannot have such a solution.

Thus, the equation has the solutions


x=3+n ( n an arbitrary integer).

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