From Förberedande kurs i matematik 1

Revision as of 10:34, 29 September 2008 (edit) Ian (Talk | contribs) ← Previous diff		Current revision (13:14, 9 October 2008) (edit) (undo) Tek (Talk | contribs) m
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-	If we write the angle	+	If we write the angle <math>\frac{7\pi }{5}</math> as
-	<math>\frac{7\pi }{5}</math>	+
-	as	+
		+	{{Displayed math||<math>\frac{7\pi}{5} = \frac{5\pi+2\pi}{5} = \pi + \frac{2\pi }{5}</math>}}
-	<math>\frac{7\pi }{5}=\frac{5\pi +2\pi }{5}=\pi +\frac{2\pi }{5}</math>	+	we see that <math>7\pi/5</math> is an angle in the third quadrant.
		+	[[Image:4_3_2_b.gif||center]]
-	we see that	+	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.
-	<math>\frac{7\pi }{5}</math>	+
-	is an angle in the third quadrant.	+
-	<center> [[Image:4_3_2_b.gif]] </center>	+	{{Displayed math||<math>v = \pi -\frac{2\pi}{5} = \frac{3\pi}{5}\,\textrm{.}</math>}}
-		+
-		+
-	the line	+
-	<math>x=\cos \frac{7\pi }{5}</math>	+
-		+
-	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	+
-	<math>x</math>	+
-	-axis, i.e.	+
-	<math>v=\pi -\frac{2\pi }{5}=\frac{3\pi }{5}</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{.}