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Solution 4.2:5a
From Förberedande kurs i matematik 1
Because
= 90
+45
We can determine the point on the unit circle which corresponds to
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}}.