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Solution 4.2:5a

From Förberedande kurs i matematik 1

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m (Lösning 4.2:5a moved to Solution 4.2:5a: Robot: moved page)
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{{NAVCONTENT_START}}
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Because
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<center> [[Image:4_2_5a.gif]] </center>
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<math>\text{135}^{\circ }\text{ }=\text{ 9}0^{\circ }\text{ }+\text{45}^{\circ }</math>,
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{{NAVCONTENT_STOP}}
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<math>\text{135}^{\circ }\text{ }</math>
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is an angle in the second quadrant which makes an angle of
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<math>\text{45}^{\circ }</math>
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with the positive
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<math>y</math>
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-axis.
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[[Image:4_2_5_a1.gif|center]]
[[Image:4_2_5_a1.gif|center]]
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We can determine the point on the unit circle which corresponds to
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<math>\text{135}^{\circ }\text{ }</math>
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by introducing an auxiliary triangle and calculating its edges using trigonometry.
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[[Image:4_2_5_a2.gif|center]]
[[Image:4_2_5_a2.gif|center]]
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opposite<math>=1\centerdot \sin \centerdot 45^{\circ }=\frac{1}{\sqrt{2}}</math>
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adjacent
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<math>=1\centerdot \cos \centerdot 45^{\circ }=\frac{1}{\sqrt{2}}</math>
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The coordinates of the point are
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<math>\left( -\frac{1}{\sqrt{2}} \right.,\left. \frac{1}{\sqrt{2}} \right)</math>
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and this shows that
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<math>\text{cos135}^{\circ }=-\frac{1}{\sqrt{2}}</math>.

Revision as of 07:56, 29 September 2008

Because 135 = 90 +45, 135 is an angle in the second quadrant which makes an angle of 45 with the positive y -axis.


We can determine the point on the unit circle which corresponds to 135 by introducing an auxiliary triangle and calculating its edges using trigonometry.


opposite=1sin45=12

adjacent =1cos45=12


The coordinates of the point are −1212  and this shows that cos135=−12.

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