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Solution 4.2:4e

From Förberedande kurs i matematik 1

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m (Lösning 4.2:4e moved to Solution 4.2:4e: Robot: moved page)
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{{NAVCONTENT_START}}
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If we write the angle
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<center> [[Image:4_2_4e.gif]] </center>
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<math>\frac{7\pi }{6}</math>
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{{NAVCONTENT_STOP}}
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as
 +
 
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<math>\frac{7\pi }{6}=\frac{6\pi +\pi }{6}=\pi +\frac{\pi }{6}</math>
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we see that the angle
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<math>\frac{7\pi }{6}</math>
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on a unit circle is in the third quadrant and makes an angle
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<math>\frac{\pi }{6}</math>
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with the negative
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<math>x</math>
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-axis.
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[[Image:4_2_4_e1.gif|center]]
[[Image:4_2_4_e1.gif|center]]
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 +
Geometrically,
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<math>\tan \frac{7\pi }{6}</math>
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is defined as the gradient of the line having an angle
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<math>\frac{7\pi }{6}</math>
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and, because this line has the same slope as the line having angle
 +
<math>\frac{\pi }{6}</math>, we have that
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 +
<math>\tan \frac{7\pi }{6}=\tan \frac{\pi }{6}=\frac{\sin \frac{\pi }{6}}{\cos \frac{\pi }{6}}=\frac{\frac{1}{2}}{\frac{\sqrt{3}}{2}}=\frac{1}{\sqrt{3}}</math>
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[[Image:4_2_4_e2.gif|center]]
[[Image:4_2_4_e2.gif|center]]

Revision as of 13:23, 28 September 2008

If we write the angle 67 as

67=66+=+6

we see that the angle 67 on a unit circle is in the third quadrant and makes an angle 6 with the negative x -axis.

Geometrically, tan67 is defined as the gradient of the line having an angle 67 and, because this line has the same slope as the line having angle 6, we have that

tan67=tan6=sin6cos6=2123=13


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