Solution 4.3:3b

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Current revision (13:23, 9 October 2008) (edit) (undo)
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The angle
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The angle <math>\pi-v</math> makes the same angle with the negative ''x''-axis as the angle <math>v</math> makes with the positive ''x''-axis and this means that <math>\pi-v</math> is the reflection of <math>v</math> in the ''y''-axis.
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<math>\pi -v\text{ }</math>
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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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Under such reflection, the angle's ''y''-coordinate does not change (but the ''x''-coordinate changes sign) and therefore <math>\sin (\pi-v) = \sin v = a\,</math>.
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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>.
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Current revision

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

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

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