Solution 4.2:3f

From Förberedande kurs i matematik 1

(Difference between revisions)
Jump to: navigation, search
m (Lösning 4.2:3f moved to Solution 4.2:3f: Robot: moved page)
Line 1: Line 1:
-
{{NAVCONTENT_START}}
+
The point on the unit circle which corresponds to the angle
-
<center> [[Image:4_2_3f-1(2).gif]] </center>
+
<math>-{\pi }/{6}\;</math>
-
{{NAVCONTENT_STOP}}
+
lies in the fourth quadrant.
-
{{NAVCONTENT_START}}
+
-
<center> [[Image:4_2_3f-2(2).gif]] </center>
+
-
{{NAVCONTENT_STOP}}
+
[[Image:4_2_3_f1.gif]]
[[Image:4_2_3_f1.gif]]
 +
 +
As usual,
 +
<math>\cos \left( -{\pi }/{6}\; \right)</math>
 +
gives the
 +
<math>x</math>
 +
-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_f2.gif]]
[[Image:4_2_3_f2.gif]]
 +
 +
We can determine the edges in this triangle by simple trigonometry and then translate these over to the point's coordinates.
[[Image:4_2_3_f3.gif]]
[[Image:4_2_3_f3.gif]]
 +
 +
The coordinates of the point of intersection are
 +
<math>\left( \frac{\sqrt{3}}{2} \right.,\left. -\frac{1}{2} \right)</math>
 +
and in particular
 +
<math>\cos \left( -{\pi }/{6}\; \right)=\frac{\sqrt{3}}{2}</math>.

Revision as of 12:35, 28 September 2008

The point on the unit circle which corresponds to the angle \displaystyle -{\pi }/{6}\; lies in the fourth quadrant.

Image:4_2_3_f1.gif

As usual, \displaystyle \cos \left( -{\pi }/{6}\; \right) gives the \displaystyle 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_f2.gif

We can determine the edges in this triangle by simple trigonometry and then translate these over to the point's coordinates.

Image:4_2_3_f3.gif

The coordinates of the point of intersection are \displaystyle \left( \frac{\sqrt{3}}{2} \right.,\left. -\frac{1}{2} \right) and in particular \displaystyle \cos \left( -{\pi }/{6}\; \right)=\frac{\sqrt{3}}{2}.

Retrieved from "http://wiki.math.se/wikis/2008/bridgecourse1-ImperialCollege/index.php/Solution_4.2:3f"