Solution 4.3:3e

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Current revision (12:22, 10 October 2008) (edit) (undo)
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The angle
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The angle <math>\pi/2+v</math> makes the same angle with the positive ''y''-axis as the angle ''v'' makes with the positive ''x''-axis, and hence we see that the ''x''-coordinate for <math>\pi/2+v</math> is equal to the ''y''-coordinate for ''v'', but with a change of sign, i.e.
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<math>\frac{\pi }{2}+v</math>
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makes the same angle with the positive
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<math>y</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 hence we see that the
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<math>x</math>
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-coordinate for
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<math>\frac{\pi }{2}+v</math>
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is equal to the
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<math>y</math>
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-coordinate for
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<math>v</math>, but with a change of sign, i.e.
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{{Displayed math||<math>\cos \Bigl(\frac{\pi}{2}+v\Bigr) = -\sin v = -a\,\textrm{.}</math>}}
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<math>\cos \left( \frac{\pi }{2}+v \right)=-\sin v=-a</math>
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{| align="center"
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|align="center"|[[Image:4_3_3_e-1.gif|center]]
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[[Image:4_3_3_e-1.gif|center]][[Image:4_3_3_e-2.gif|center]]
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|align="center"|[[Image:4_3_3_e-2.gif|center]]
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|-
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|align="center"|<small>Angle ''v''</small>
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angle
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|align="center"|<small>Angle π/2&nbsp;+&nbsp;''v''</small>
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<math>v</math>
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|}
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angle
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<math>\frac{\pi }{2}+v</math>
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Current revision

The angle \displaystyle \pi/2+v makes the same angle with the positive y-axis as the angle v makes with the positive x-axis, and hence we see that the x-coordinate for \displaystyle \pi/2+v is equal to the y-coordinate for v, but with a change of sign, i.e.

\displaystyle \cos \Bigl(\frac{\pi}{2}+v\Bigr) = -\sin v = -a\,\textrm{.}
Angle v Angle π/2 + v
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