Solution 4.3:2b

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m (Lösning 4.3:2b moved to Solution 4.3:2b: Robot: moved page)
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{{NAVCONTENT_START}}
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If we write the angle
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<math>\frac{7\pi }{5}</math>
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as
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<math>\frac{7\pi }{5}=\frac{5\pi +2\pi }{5}=\pi +\frac{2\pi }{5}</math>
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we see that
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<math>\frac{7\pi }{5}</math>
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is an angle in the third quadrant.
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<center> [[Image:4_3_2_b.gif]] </center>
<center> [[Image:4_3_2_b.gif]] </center>
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<center> [[Image:4_3_2b.gif]] </center>
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{{NAVCONTENT_STOP}}
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the line
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<math>x=\cos \frac{7\pi }{5}</math>
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The angle between
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<math>0</math>
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and
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<math>\pi </math>
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which has the same x-coordinate as the angle
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<math>{7\pi }/{5}\;</math>, and hence the same cosine value, is the reflection of the angle
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<math>{7\pi }/{5}\;</math>
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in the
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<math>x</math>
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-axis, i.e.
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<math>v=\pi -\frac{2\pi }{5}=\frac{3\pi }{5}</math>.

Revision as of 10:34, 29 September 2008

If we write the angle \displaystyle \frac{7\pi }{5} as


\displaystyle \frac{7\pi }{5}=\frac{5\pi +2\pi }{5}=\pi +\frac{2\pi }{5}


we see that \displaystyle \frac{7\pi }{5} is an angle in the third quadrant.

Image:4_3_2_b.gif


the line \displaystyle x=\cos \frac{7\pi }{5}

The angle between \displaystyle 0 and \displaystyle \pi which has the same x-coordinate as the angle \displaystyle {7\pi }/{5}\;, and hence the same cosine value, is the reflection of the angle \displaystyle {7\pi }/{5}\; in the \displaystyle x -axis, i.e. \displaystyle v=\pi -\frac{2\pi }{5}=\frac{3\pi }{5}.

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