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Solution 4.3:3b

From Förberedande kurs i matematik 1

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m (Lösning 4.3:3b moved to Solution 4.3:3b: Robot: moved page)
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{{NAVCONTENT_START}}
+
The angle
-
<center> [[Image:4_3_3b.gif]] </center>
+
<math>\pi -v\text{ }</math>
-
{{NAVCONTENT_STOP}}
+
makes the same angle with the negative
 +
<math>x</math>
 +
-axis as the angle
 +
<math>v</math>
 +
makes with the positive
 +
<math>x</math>
 +
-axis and this means that
 +
<math>\pi -v\text{ }</math>
 +
is the reflection of
 +
<math>v</math>
 +
in the y-axis.
 +
 
[[Image:4_3_3_b.gif|center]]
[[Image:4_3_3_b.gif|center]]
 +
 +
Under such reflection, the angle's
 +
<math>y</math>
 +
-coordinate does not change (but the
 +
<math>x</math>
 +
-coordinate changes sign) and therefore
 +
<math>\text{sin}\left( \pi -v \right)=\text{sin }v\text{ }=a</math>.

Revision as of 10:51, 29 September 2008

The angle −v makes the same angle with the negative x -axis as the angle v makes with the positive x -axis and this means that −v is the reflection of v in the y-axis.

Under such reflection, the angle's y -coordinate does not change (but the x -coordinate changes sign) and therefore sin−v=sin v =a .

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