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Solution 4.1:1

From Förberedande kurs i matematik 1

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Current revision (07:10, 3 October 2008) (edit) (undo)
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The only thing we really need to remember is that one turn corresponds to
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The only thing we really need to remember is that one revolution corresponds to
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<math>\text{36}0^{\text{o}}</math>
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360° or <math>2\pi</math> radians. Then we get:
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or
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<math>\text{2}\pi </math>
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radians. Then we get:
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a)
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{|
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<math>\frac{1}{4}</math>
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||a)&nbsp;&nbsp;
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turn
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|width="100%"|<math>\frac{1}{4}\ \text{revolution} = \frac{1}{4}\cdot 360^{\circ} = 90^{\circ}</math> and
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<math>=\frac{1}{4}\centerdot 360^{\circ }=90^{\circ }</math>
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|-
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and
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||
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|width="100%"|<math>\frac{1}{4}\ \text{revolution} = \frac{1}{4}\cdot 2\pi\ \text{radians} = \frac{\pi}{2}\ \text{radians,}</math>
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<math>\frac{1}{4}</math>
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|-
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turn
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|height="10px"|&nbsp;
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<math>=\frac{1}{4}\centerdot 2\pi </math>
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|-
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radians
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||b)&nbsp;&nbsp;
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<math>=\frac{\pi }{2}</math>
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|width="100%"|<math>\frac{3}{8}\ \text{revolution} = \frac{3}{8}\cdot 360^{\circ} = 135^{\circ}</math> and
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radians,
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|-
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||
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||<math>\frac{3}{8}\ \text{revolution} = \frac{3}{8}\cdot 2\pi\ \text{radians} = \frac{3\pi}{4}\ \text{radians,}</math>
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b)
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|-
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<math>\frac{3}{8}</math>
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|height="10px"|&nbsp;
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turn
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|-
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<math>=\frac{3}{8}\centerdot 360^{\circ }=135^{\circ }</math>
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||c)&nbsp;&nbsp;
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and
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|width="100%"|<math>-\frac{2}{3}\ \text{revolution} = -\frac{2}{3}\cdot 360^{\circ} = -240^{\circ}</math> and
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|-
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<math>\frac{3}{8}</math>
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||
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turn
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|width="100%"|<math>-\frac{2}{3}\ \text{revolution} = -\frac{2}{3}\cdot 2\pi\ \text{radians} = -\frac{4\pi}{3}\ \text{radians,}</math>
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<math>=\frac{3}{8}\centerdot 2\pi </math>
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|-
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radians
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|height="10px"|&nbsp;
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<math>=\frac{3\pi }{4}</math>
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|-
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radians,
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||d)&nbsp;&nbsp;
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|width="100%"|<math>\frac{97}{12}\ \text{revolution} = \frac{97}{12}\cdot 360^{\circ} = 2910^{\circ}</math> and
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|-
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||
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c)
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|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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<math>-\frac{2}{3}</math>
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|}
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turn
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<math>=-\frac{2}{3}\centerdot 360^{\circ }=-240^{\circ }</math>
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and
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<math>-\frac{2}{3}</math>
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turn
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<math>=-\frac{2}{3}\centerdot 2\pi </math>
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radians
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<math>=-\frac{4\pi }{3}</math>
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radians,
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d)
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<math>\frac{97}{12}</math>
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turn
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<math>=\frac{97}{12}\centerdot 360^{\circ }=2910^{\circ }</math>
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and
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<math>\frac{97}{12}</math>
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turn
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<math>=\frac{97}{12}\centerdot 2\pi </math>
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radians
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<math>=\frac{97\pi }{6}</math>
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radians,
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Current revision

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

a)   41 revolution=41360=90 and
41 revolution=412 radians=2 radians,
 
b)   83 revolution=83360=135 and
83 revolution=832 radians=43 radians,
 
c)   −32 revolution=−32360=−240 and
−32 revolution=−322 radians=−34 radians,
 
d)   1297 revolution=1297360=2910 and
1297 revolution=12972 radians=697 radians.
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