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Solution 4.2:3d

From Förberedande kurs i matematik 1

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m (Lösning 4.2:3d moved to Solution 4.2:3d: Robot: moved page)
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{{NAVCONTENT_START}}
+
In order to get an angle between
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<center> [[Image:4_2_3d.gif]] </center>
+
<math>0</math>
-
{{NAVCONTENT_STOP}}
+
and
 +
<math>\text{2}\pi </math>, we subtract
 +
<math>\text{2}\pi </math>
 +
from
 +
<math>{7\pi }/{2}\;</math>
 +
, which also leaves the cosine value unchanged
 +
 
 +
 
 +
<math>\cos \frac{7\pi }{2}=\cos \left( \frac{7\pi }{2}-2\pi \right)=\cos \frac{3\pi }{2}</math>
 +
 
 +
 
 +
When we draw a line which makes an angle
 +
<math>{3\pi }/{2}\;</math>
 +
with the positive
 +
<math>x</math>
 +
-axis, we get the negative
 +
<math>y</math>
 +
-axis and we see that this line cuts the unit circle at the point
 +
<math>\left( 0 \right.,\left. -1 \right)</math>. The
 +
<math>x</math>
 +
-coordinate of the intersection point is thus
 +
<math>0</math>
 +
and hence
 +
<math>\cos {7\pi }/{2}\;=\cos {3\pi }/{2}\;=0</math>
 +
 
 +
 
 +
 
[[Image:4_2_3_d.gif|center]]
[[Image:4_2_3_d.gif|center]]

Revision as of 12:06, 28 September 2008

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


cos27=cos27−2=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 cos72=cos32=0


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