Solution 4.3:1b

From Förberedande kurs i matematik 1

(Difference between revisions)
Jump to: navigation, search
m (Lösning 4.3:1b moved to Solution 4.3:1b: Robot: moved page)
Line 1: Line 1:
-
{{NAVCONTENT_START}}
+
Because the sine value for an angle is equal to the angle's
-
<center> [[Image:4_3_1_b.gif]] </center>
+
<math>y</math>
 +
-coordinate on a unit circle, two angles have the same sine value only if they have the same <math>y</math>-coordinate. Therefore, if we draw in the angle
 +
<math>{\pi }/{7}\;</math>
 +
on a unit circle, we see that the only angle between
 +
<math>{\pi }/{2}\;</math>
 +
and
 +
<math>\pi </math>
 +
which has the same sine value lies in the second quadrant, where the line
 +
<math>{y=\sin \pi }/{7}\;</math>
 +
cuts the unit circle.
-
<center> [[Image:4_3_1b.gif]] </center>
+
 
-
{{NAVCONTENT_STOP}}
+
FIGURE1 FIGURE2
 +
the line
 +
<math>{y=\sin \pi }/{7}\;</math>
 +
the line
 +
<math>{y=\sin \pi }/{7}\;</math>
 +
 
 +
 
 +
Because of symmetry, we have that this angle is the reflection of the angle
 +
<math>{\pi }/{7}\;</math>
 +
in the
 +
<math>y</math>-axis, i.e.
 +
 
 +
<math>v=\pi -{\pi }/{7}\;={6\pi }/{7}\;</math>.

Revision as of 11:59, 12 September 2008

Because the sine value for an angle is equal to the angle's \displaystyle y -coordinate on a unit circle, two angles have the same sine value only if they have the same \displaystyle y-coordinate. Therefore, if we draw in the angle \displaystyle {\pi }/{7}\; on a unit circle, we see that the only angle between \displaystyle {\pi }/{2}\; and \displaystyle \pi which has the same sine value lies in the second quadrant, where the line \displaystyle {y=\sin \pi }/{7}\; cuts the unit circle.


FIGURE1 FIGURE2 the line \displaystyle {y=\sin \pi }/{7}\; the line \displaystyle {y=\sin \pi }/{7}\;


Because of symmetry, we have that this angle is the reflection of the angle \displaystyle {\pi }/{7}\; in the \displaystyle y-axis, i.e.

\displaystyle v=\pi -{\pi }/{7}\;={6\pi }/{7}\;.

Retrieved from "http://wiki.sommarmatte.se/wikis/2008/bridgecourse1-ImperialCollege/index.php/Solution_4.3:1b"