Solution 4.3:3b
From Förberedande kurs i matematik 1
(Difference between revisions)
m (Lösning 4.3:3b moved to Solution 4.3:3b: Robot: moved page) |
|||
Line 1: | Line 1: | ||
- | { | + | The angle |
- | < | + | <math>\pi -v\text{ }</math> |
- | { | + | 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 \displaystyle \pi -v\text{ } makes the same angle with the negative \displaystyle x -axis as the angle \displaystyle v makes with the positive \displaystyle x -axis and this means that \displaystyle \pi -v\text{ } is the reflection of \displaystyle v in the y-axis.
Under such reflection, the angle's \displaystyle y -coordinate does not change (but the \displaystyle x -coordinate changes sign) and therefore \displaystyle \text{sin}\left( \pi -v \right)=\text{sin }v\text{ }=a.