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Solution 4.2:3d

From Förberedande kurs i matematik 1

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Current revision (07:57, 9 October 2008) (edit) (undo)
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In order to get an angle between <math>0</math> and <math>\text{2}\pi</math>, we subtract <math>2\pi</math> from <math>{7\pi }/{2}\,</math>, which also leaves the cosine value unchanged
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<center> [[Bild:4_2_3d.gif]] </center>
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{{Displayed math||<math>\cos\frac{7\pi}{2} = \cos\Bigl(\frac{7\pi}{2}-2\pi\Bigr) = \cos\frac{3\pi}{2}\,\textrm{.}</math>}}
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When we draw a line which makes an angle <math>3\pi/2</math> with the positive ''x''-axis, we get the negative ''y''-axis and we see that this line cuts the unit circle at the point (0,-1). The ''x''-coordinate of the intersection point is thus
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<math>0</math> and hence <math>\cos (7\pi/2) = \cos (3\pi/2) = 0\,</math>.
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[[Image:4_2_3_d.gif|center]]

Current revision

In order to get an angle between 0 and 2, we subtract 2 from 72, which also leaves the cosine value unchanged

cos27=cos272=cos23. 

When we draw a line which makes an angle 32 with the positive x-axis, we get the negative y-axis and we see that this line cuts the unit circle at the point (0,-1). The x-coordinate of the intersection point is thus 0 and hence cos(72)=cos(32)=0.