From Förberedande kurs i matematik 1

Revision as of 08:02, 3 April 2008 (edit) Oskar (Talk | contribs) (Ny sida: {{NAVCONTENT_START}} <center> Bild:4_2_4e.gif </center> {{NAVCONTENT_STOP}}) ← Previous diff		Current revision (10:44, 9 October 2008) (edit) (undo) Tek (Talk | contribs) m
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-	{{NAVCONTENT_START}}	+	If we write the angle <math>\frac{7\pi}{6}</math> as
-	<center> [[Bild:4_2_4e.gif]] </center>	+
-	{{NAVCONTENT_STOP}}	+	{{Displayed math||<math>\frac{7\pi}{6} = \frac{6\pi+\pi}{6} = \pi + \frac{\pi }{6}</math>}}
		+
		+	we see that the angle <math>7\pi/6</math> on the unit circle is in the third quadrant and makes an angle <math>\pi/6</math> with the negative ''x''-axis.
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		+	[[Image:4_2_4_e1.gif|center]]
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		+	Geometrically, <math>\tan (7\pi/6)</math> is defined as the slope of the line having an angle <math>7\pi/6</math> and, because this line has the same slope as the line having angle <math>\pi/6</math>, we have that
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		+	{{Displayed math||<math>\tan\frac{7\pi}{6} = \tan\frac{\pi}{6} = \frac{\sin\dfrac{\pi }{6}}{\cos\dfrac{\pi }{6}} = \frac{\dfrac{1}{2}}{\dfrac{\sqrt{3}}{2}} = \frac{1}{\sqrt{3}}\,\textrm{.}</math>}}
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		+	[[Image:4_2_4_e2.gif|center]]

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Current revision

If we write the angle \displaystyle \frac{7\pi}{6} as

\displaystyle \frac{7\pi}{6} = \frac{6\pi+\pi}{6} = \pi + \frac{\pi }{6}

we see that the angle \displaystyle 7\pi/6 on the unit circle is in the third quadrant and makes an angle \displaystyle \pi/6 with the negative x-axis.

Geometrically, \displaystyle \tan (7\pi/6) is defined as the slope of the line having an angle \displaystyle 7\pi/6 and, because this line has the same slope as the line having angle \displaystyle \pi/6, we have that

\displaystyle \tan\frac{7\pi}{6} = \tan\frac{\pi}{6} = \frac{\sin\dfrac{\pi }{6}}{\cos\dfrac{\pi }{6}} = \frac{\dfrac{1}{2}}{\dfrac{\sqrt{3}}{2}} = \frac{1}{\sqrt{3}}\,\textrm{.}