From Förberedande kurs i matematik 1

Revision as of 12:51, 2 April 2008 (edit) Oskar (Talk | contribs) (Ny sida: {{NAVCONTENT_START}} <center> Bild:4_1_1a.gif </center> {{NAVCONTENT_STOP}}) ← Previous diff		Current revision (07:10, 3 October 2008) (edit) (undo) Tek (Talk | contribs) m
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-	{{NAVCONTENT_START}}	+	The only thing we really need to remember is that one revolution corresponds to
-	<center> [[Bild:4_1_1a.gif]] </center>	+	360° or <math>2\pi</math> radians. Then we get:
-	{{NAVCONTENT_STOP}}	+
		+	{|
		+	||a)&nbsp;&nbsp;
		+	|width="100%"|<math>\frac{1}{4}\ \text{revolution} = \frac{1}{4}\cdot 360^{\circ} = 90^{\circ}</math> and
		+	|-
		+	||
		+	|width="100%"|<math>\frac{1}{4}\ \text{revolution} = \frac{1}{4}\cdot 2\pi\ \text{radians} = \frac{\pi}{2}\ \text{radians,}</math>
		+	|-
		+	|height="10px"|&nbsp;
		+	|-
		+	||b)&nbsp;&nbsp;
		+	|width="100%"|<math>\frac{3}{8}\ \text{revolution} = \frac{3}{8}\cdot 360^{\circ} = 135^{\circ}</math> and
		+	|-
		+	||
		+	||<math>\frac{3}{8}\ \text{revolution} = \frac{3}{8}\cdot 2\pi\ \text{radians} = \frac{3\pi}{4}\ \text{radians,}</math>
		+	|-
		+	|height="10px"|&nbsp;
		+	|-
		+	||c)&nbsp;&nbsp;
		+	|width="100%"|<math>-\frac{2}{3}\ \text{revolution} = -\frac{2}{3}\cdot 360^{\circ} = -240^{\circ}</math> and
		+	|-
		+	||
		+	|width="100%"|<math>-\frac{2}{3}\ \text{revolution} = -\frac{2}{3}\cdot 2\pi\ \text{radians} = -\frac{4\pi}{3}\ \text{radians,}</math>
		+	|-
		+	|height="10px"|&nbsp;
		+	|-
		+	||d)&nbsp;&nbsp;
		+	|width="100%"|<math>\frac{97}{12}\ \text{revolution} = \frac{97}{12}\cdot 360^{\circ} = 2910^{\circ}</math> and
		+	|-
		+	||
		+	|width="100%"|<math>\frac{97}{12}\ \text{revolution} = \frac{97}{12}\cdot 2\pi\ \text{radians} = \frac{97\pi}{6}\ \text{radians.}</math>
		+	|}

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Current revision

The only thing we really need to remember is that one revolution corresponds to 360° or \displaystyle 2\pi radians. Then we get:

a)	\displaystyle \frac{1}{4}\ \text{revolution} = \frac{1}{4}\cdot 360^{\circ} = 90^{\circ} and
	\displaystyle \frac{1}{4}\ \text{revolution} = \frac{1}{4}\cdot 2\pi\ \text{radians} = \frac{\pi}{2}\ \text{radians,}
b)	\displaystyle \frac{3}{8}\ \text{revolution} = \frac{3}{8}\cdot 360^{\circ} = 135^{\circ} and
	\displaystyle \frac{3}{8}\ \text{revolution} = \frac{3}{8}\cdot 2\pi\ \text{radians} = \frac{3\pi}{4}\ \text{radians,}
c)	\displaystyle -\frac{2}{3}\ \text{revolution} = -\frac{2}{3}\cdot 360^{\circ} = -240^{\circ} and
	\displaystyle -\frac{2}{3}\ \text{revolution} = -\frac{2}{3}\cdot 2\pi\ \text{radians} = -\frac{4\pi}{3}\ \text{radians,}
d)	\displaystyle \frac{97}{12}\ \text{revolution} = \frac{97}{12}\cdot 360^{\circ} = 2910^{\circ} and
	\displaystyle \frac{97}{12}\ \text{revolution} = \frac{97}{12}\cdot 2\pi\ \text{radians} = \frac{97\pi}{6}\ \text{radians.}