Solution 4.3:3b

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m (Lösning 4.3:3b moved to Solution 4.3:3b: Robot: moved page)
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{{NAVCONTENT_START}}
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The angle
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<center> [[Image:4_3_3b.gif]] </center>
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<math>\pi -v\text{ }</math>
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{{NAVCONTENT_STOP}}
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makes the same angle with the negative
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<math>x</math>
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-axis as the angle
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<math>v</math>
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makes with the positive
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<math>x</math>
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-axis and this means that
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<math>\pi -v\text{ }</math>
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is the reflection of
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<math>v</math>
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in the y-axis.
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[[Image:4_3_3_b.gif|center]]
[[Image:4_3_3_b.gif|center]]
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Under such reflection, the angle's
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<math>y</math>
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-coordinate does not change (but the
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<math>x</math>
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-coordinate changes sign) and therefore
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<math>\text{sin}\left( \pi -v \right)=\text{sin }v\text{ }=a</math>.

Revision as of 10:51, 29 September 2008

The angle \displaystyle \pi -v\text{ } makes the same angle with the negative \displaystyle x -axis as the angle \displaystyle v makes with the positive \displaystyle x -axis and this means that \displaystyle \pi -v\text{ } is the reflection of \displaystyle v in the y-axis.

Under such reflection, the angle's \displaystyle y -coordinate does not change (but the \displaystyle x -coordinate changes sign) and therefore \displaystyle \text{sin}\left( \pi -v \right)=\text{sin }v\text{ }=a.

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