Solution 4.4:1d

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Current revision (13:16, 10 October 2008) (edit) (undo)
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Because
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Because <math>\tan v = \frac{\sin v}{\cos v}</math>, the condition <math>\tan v = 1</math> gives <math>\sin v = \cos v</math>, i.e. we look for angles in the unit circle whose ''x''- and ''y''-coordinates are equal.
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<math>\tan v=\frac{\sin v}{\cos v}</math>, the condition
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<math>\text{tan }v=\text{1 }</math>
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gives
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<math>\text{sin }v=\text{ cos }v</math>, i.e. we look for angles in the unit circle whose
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<math>x</math>
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<math>y</math>
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-coordinates are equal.
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After drawing the unit circle and the line y=x, we see that there are two angles which satisfy these conditions,
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<math>v={\pi }/{4}\;</math>
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and
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<math>v=\pi +{\pi }/{4}\;={5\pi }/{4}\;</math>
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After drawing the unit circle and the line y=x, we see that there are two angles which satisfy these conditions, <math>v=\pi/4</math> and <math>v = \pi + \pi/4 = 5\pi/4\,</math>.
[[Image:4_4_1_d.gif|center]]
[[Image:4_4_1_d.gif|center]]

Current revision

Because \displaystyle \tan v = \frac{\sin v}{\cos v}, the condition \displaystyle \tan v = 1 gives \displaystyle \sin v = \cos v, i.e. we look for angles in the unit circle whose x- and y-coordinates are equal.

After drawing the unit circle and the line y=x, we see that there are two angles which satisfy these conditions, \displaystyle v=\pi/4 and \displaystyle v = \pi + \pi/4 = 5\pi/4\,.

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