Solution 4.4:1d

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m (Lösning 4.4:1d moved to Solution 4.4:1d: Robot: moved page)
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Because
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<center> [[Image:4_4_1d.gif]] </center>
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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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- and
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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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[[Image:4_4_1_d.gif|center]]
[[Image:4_4_1_d.gif|center]]

Revision as of 12:38, 30 September 2008

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