Solution 4.4:1b

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m (Lösning 4.4:1b moved to Solution 4.4:1b: Robot: moved page)
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{{NAVCONTENT_START}}
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The easiest angle to find is
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<center> [[Image:4_4_1b.gif]] </center>
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<math>v={\pi }/{3}\;</math>
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{{NAVCONTENT_STOP}}
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in the first quadrant. When we draw the unit circle, we see that the angle which makes the same angle with the positive
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<math>x</math>
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-axis as
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<math>v={\pi }/{3}\;</math>, but is under the
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<math>x</math>
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-axis, also has a cosine value of
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<math>{1}/{2}\;</math>
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(same
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<math>x</math>
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-coordinate).
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[[Image:4_4_1_b.gif|center]]
[[Image:4_4_1_b.gif|center]]
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There are thus two angles,
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<math>v={\pi }/{3}\;</math>
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and
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<math>v=2\pi -{\pi }/{3}\;={5\pi }/{3}\;</math>
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which have their cosine value equal to
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<math>\frac{1}{2}</math>.

Revision as of 12:31, 30 September 2008

The easiest angle to find is \displaystyle v={\pi }/{3}\; in the first quadrant. When we draw the unit circle, we see that the angle which makes the same angle with the positive \displaystyle x -axis as \displaystyle v={\pi }/{3}\;, but is under the \displaystyle x -axis, also has a cosine value of \displaystyle {1}/{2}\; (same \displaystyle x -coordinate).


There are thus two angles, \displaystyle v={\pi }/{3}\; and \displaystyle v=2\pi -{\pi }/{3}\;={5\pi }/{3}\; which have their cosine value equal to \displaystyle \frac{1}{2}.

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