From Förberedande kurs i matematik 1

Revision as of 09:42, 3 April 2008 (edit) Oskar (Talk | contribs) (Ny sida: {{NAVCONTENT_START}} <center> Bild:4_3_2b.gif </center> {{NAVCONTENT_STOP}}) ← Previous diff		Current revision (13:14, 9 October 2008) (edit) (undo) Tek (Talk | contribs) m
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-	{{NAVCONTENT_START}}	+	If we write the angle <math>\frac{7\pi }{5}</math> as
-	<center> [[Bild:4_3_2b.gif]] </center>	+
-	{{NAVCONTENT_STOP}}	+	{{Displayed math||<math>\frac{7\pi}{5} = \frac{5\pi+2\pi}{5} = \pi + \frac{2\pi }{5}</math>}}
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		+	we see that <math>7\pi/5</math> is an angle in the third quadrant.
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		+	[[Image:4_3_2_b.gif||center]]
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		+	The angle between <math>0</math> and <math>\pi</math> which has the same ''x''-coordinate as the angle <math>7\pi/5</math>, and hence the same cosine value, is the reflection of the angle <math>7\pi/5</math> in the ''x''-axis, i.e.
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		+	{{Displayed math||<math>v = \pi -\frac{2\pi}{5} = \frac{3\pi}{5}\,\textrm{.}</math>}}

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Current revision

If we write the angle \displaystyle \frac{7\pi }{5} as

\displaystyle \frac{7\pi}{5} = \frac{5\pi+2\pi}{5} = \pi + \frac{2\pi }{5}

we see that \displaystyle 7\pi/5 is an angle in the third quadrant.

The angle between \displaystyle 0 and \displaystyle \pi which has the same x-coordinate as the angle \displaystyle 7\pi/5, and hence the same cosine value, is the reflection of the angle \displaystyle 7\pi/5 in the x-axis, i.e.

\displaystyle v = \pi -\frac{2\pi}{5} = \frac{3\pi}{5}\,\textrm{.}