Solution 4.2:3d
From Förberedande kurs i matematik 1
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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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- | + | {{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 | ||
+ | <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]] | [[Image:4_2_3_d.gif|center]] |
Current revision
In order to get an angle between \displaystyle 0 and \displaystyle \text{2}\pi, we subtract \displaystyle 2\pi from \displaystyle {7\pi }/{2}\,, which also leaves the cosine value unchanged
\displaystyle \cos\frac{7\pi}{2} = \cos\Bigl(\frac{7\pi}{2}-2\pi\Bigr) = \cos\frac{3\pi}{2}\,\textrm{.} |
When we draw a line which makes an angle \displaystyle 3\pi/2 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 \displaystyle 0 and hence \displaystyle \cos (7\pi/2) = \cos (3\pi/2) = 0\,.