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Solution 4.2:5a

From Förberedande kurs i matematik 1

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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\displaystyle =1\centerdot \sin \centerdot 45^{\circ }=\frac{1}{\sqrt{2}}

adjacent \displaystyle =1\centerdot \cos \centerdot 45^{\circ }=\frac{1}{\sqrt{2}}


The coordinates of the point are \displaystyle \left( -\frac{1}{\sqrt{2}} \right.,\left. \frac{1}{\sqrt{2}} \right) and this shows that \displaystyle \text{cos135}^{\circ }=-\frac{1}{\sqrt{2}}.