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Solution 4.1:1

From Förberedande kurs i matematik 1

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m (Lösning 4.1:1 moved to Solution 4.1:1: Robot: moved page)
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{{NAVCONTENT_START}}
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The only thing we really need to remember is that one turn corresponds to
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<center> [[Image:4_1_1.gif]] </center>
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<math>\text{36}0^{\text{o}}</math>
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{{NAVCONTENT_STOP}}
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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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<math>\frac{1}{4}</math>
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turn
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<math>=\frac{1}{4}\centerdot 360^{\circ }=90^{\circ }</math>
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and
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<math>\frac{1}{4}</math>
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turn
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<math>=\frac{1}{4}\centerdot 2\pi </math>
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radians
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<math>=\frac{\pi }{2}</math>
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radians,
 +
 +
 
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b)
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<math>\frac{3}{8}</math>
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turn
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<math>=\frac{3}{8}\centerdot 360^{\circ }=135^{\circ }</math>
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and
 +
 +
<math>\frac{3}{8}</math>
 +
turn
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<math>=\frac{3}{8}\centerdot 2\pi </math>
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radians
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<math>=\frac{3\pi }{4}</math>
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radians,
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 +
 +
 
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c)
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<math>-\frac{2}{3}</math>
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turn
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<math>=-\frac{2}{3}\centerdot 360^{\circ }=-240^{\circ }</math>
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and
 +
 +
<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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 +
 
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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
 +
 +
<math>\frac{97}{12}</math>
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turn
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<math>=\frac{97}{12}\centerdot 2\pi </math>
 +
radians
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<math>=\frac{97\pi }{6}</math>
 +
radians,

Revision as of 12:31, 26 September 2008

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

a) 41 turn =41360=90 and

41 turn =412 radians =2 radians,


b) 83 turn =83360=135 and

83 turn =832 radians =43 radians,


c) −32 turn =−32360=−240 and

−32 turn =−322 radians =−34 radians,


d) 1297 turn =1297360=2910 and

1297 turn =12972 radians =697 radians,

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