Processing Math: Done
Solution 4.2:3f
From Förberedande kurs i matematik 1
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- | + | The point on the unit circle which corresponds to the angle <math>-\pi/6</math> lies in the fourth quadrant. | |
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- | [[Image:4_2_3_f1.gif]] | + | [[Image:4_2_3_f1.gif||center]] |
- | + | As usual, <math>\cos (-\pi/6)</math> gives the ''x''-coordinate of the point of intersection between the angle's line and the unit circle. In order to determine this point, we introduce an auxiliary triangle in the fourth quadrant. | |
- | [[Image:4_2_3_f3.gif]] | + | [[Image:4_2_3_f2.gif||center]] |
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+ | We can determine the edges in this triangle by simple trigonometry and then translate these over to the point's coordinates. | ||
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+ | {| width="100%" | ||
+ | |width="50%" align="center"|[[Image:4_2_3_f3.gif]] | ||
+ | |width="50%" align="left"|<math>\begin{align}\text{opposite} &= 1\cdot\sin\frac{\pi}{6} = \frac{1}{2}\\[5pt] \text{adjacent} &= 1\cdot\cos\frac{\pi}{6} = \frac{\sqrt{3}}{2}\end{align}</math> | ||
+ | |} | ||
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+ | The coordinates of the point of intersection are <math>(\sqrt{3}/2,-1/2)</math> and in particular <math>\cos (-\pi/6) = \sqrt{3}/2\,</math>. |
Current revision
The point on the unit circle which corresponds to the angle 6
As usual, 6)
We can determine the edges in this triangle by simple trigonometry and then translate these over to the point's coordinates.
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The coordinates of the point of intersection are 3
2
−1
2)
6)=
3
2