Solution 4.2:3b
From Förberedande kurs i matematik 1
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- | {{ | + | The angle |
- | < | + | <math>\text{2}\pi </math> |
- | + | corresponds to a whole revolution and therefore we see that if we draw in a line with angle | |
+ | <math>\text{2}\pi </math> | ||
+ | relative to the positive | ||
+ | <math>x</math> | ||
+ | -axis, we will get the positive | ||
+ | <math>x</math> | ||
+ | -axis. | ||
+ | |||
[[Image:4_2_3_b.gif|center]] | [[Image:4_2_3_b.gif|center]] | ||
+ | |||
+ | Because | ||
+ | <math>\cos \text{2}\pi </math> | ||
+ | is the | ||
+ | <math>x</math> | ||
+ | -coordinate for the point of intersection between the line with angle | ||
+ | <math>\text{2}\pi </math> | ||
+ | and the unit circle, we can see directly that | ||
+ | <math>\cos \text{2}\pi =1</math>. |
Revision as of 11:51, 28 September 2008
The angle \displaystyle \text{2}\pi corresponds to a whole revolution and therefore we see that if we draw in a line with angle \displaystyle \text{2}\pi relative to the positive \displaystyle x -axis, we will get the positive \displaystyle x -axis.
Because \displaystyle \cos \text{2}\pi is the \displaystyle x -coordinate for the point of intersection between the line with angle \displaystyle \text{2}\pi and the unit circle, we can see directly that \displaystyle \cos \text{2}\pi =1.