Solution 4.1:1

From Förberedande kurs i matematik 1

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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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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
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<math>\frac{3}{8}</math>
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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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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
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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,

Revision as of 12:31, 26 September 2008

The only thing we really need to remember is that one turn corresponds to \displaystyle \text{36}0^{\text{o}} or \displaystyle \text{2}\pi radians. Then we get:

a) \displaystyle \frac{1}{4} turn \displaystyle =\frac{1}{4}\centerdot 360^{\circ }=90^{\circ } and

\displaystyle \frac{1}{4} turn \displaystyle =\frac{1}{4}\centerdot 2\pi radians \displaystyle =\frac{\pi }{2} radians,


b) \displaystyle \frac{3}{8} turn \displaystyle =\frac{3}{8}\centerdot 360^{\circ }=135^{\circ } and

\displaystyle \frac{3}{8} turn \displaystyle =\frac{3}{8}\centerdot 2\pi radians \displaystyle =\frac{3\pi }{4} radians,


c) \displaystyle -\frac{2}{3} turn \displaystyle =-\frac{2}{3}\centerdot 360^{\circ }=-240^{\circ } and

\displaystyle -\frac{2}{3} turn \displaystyle =-\frac{2}{3}\centerdot 2\pi radians \displaystyle =-\frac{4\pi }{3} radians,


d) \displaystyle \frac{97}{12} turn \displaystyle =\frac{97}{12}\centerdot 360^{\circ }=2910^{\circ } and

\displaystyle \frac{97}{12} turn \displaystyle =\frac{97}{12}\centerdot 2\pi radians \displaystyle =\frac{97\pi }{6} radians,

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