From Förberedande kurs i matematik 1

Revision as of 09:44, 9 September 2008 (edit) Tekbot (Talk | contribs) m (Lösning 4.2:3d moved to Solution 4.2:3d: Robot: moved page) ← Previous diff		Current revision (07:57, 9 October 2008) (edit) (undo) Tek (Talk | contribs) m
(One intermediate revision not shown.)
Line 1:		Line 1:
-	{{NAVCONTENT_START}}	+	In order to get an angle between <math>0</math> and <math>\text{2}\pi</math>, we subtract <math>2\pi</math> from <math>{7\pi }/{2}\,</math>, which also leaves the cosine value unchanged
-	<center> [[Image:4_2_3d.gif]] </center>	+
-	{{NAVCONTENT_STOP}}	+	{{Displayed math||<math>\cos\frac{7\pi}{2} = \cos\Bigl(\frac{7\pi}{2}-2\pi\Bigr) = \cos\frac{3\pi}{2}\,\textrm{.}</math>}}
		+
		+	When we draw a line which makes an angle <math>3\pi/2</math> with the positive ''x''-axis, we get the negative ''y''-axis and we see that this line cuts the unit circle at the point (0,-1). The ''x''-coordinate of the intersection point is thus
		+	<math>0</math> and hence <math>\cos (7\pi/2) = \cos (3\pi/2) = 0\,</math>.
		+
	[[Image:4_2_3_d.gif|center]]		[[Image:4_2_3_d.gif|center]]

---

Current revision

In order to get an angle between \displaystyle 0 and \displaystyle \text{2}\pi, we subtract \displaystyle 2\pi from \displaystyle {7\pi }/{2}\,, which also leaves the cosine value unchanged

\displaystyle \cos\frac{7\pi}{2} = \cos\Bigl(\frac{7\pi}{2}-2\pi\Bigr) = \cos\frac{3\pi}{2}\,\textrm{.}

When we draw a line which makes an angle \displaystyle 3\pi/2 with the positive x-axis, we get the negative y-axis and we see that this line cuts the unit circle at the point (0,-1). The x-coordinate of the intersection point is thus \displaystyle 0 and hence \displaystyle \cos (7\pi/2) = \cos (3\pi/2) = 0\,.