Processing Math: Done
Solution 4.3:3d
From Förberedande kurs i matematik 1
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- | {{ | + | The expression for the angle |
- | < | + | <math>{\pi }/{2}\;-v</math> |
- | {{ | + | differs from |
+ | <math>{\pi }/{2}\;</math> | ||
+ | by as much as | ||
+ | <math>-v\text{ }</math> | ||
+ | differs from | ||
+ | <math>0</math>. This means that | ||
+ | <math>{\pi }/{2}\;</math> | ||
+ | makes the same angle with the positive | ||
+ | <math>y</math> | ||
+ | -axis as | ||
+ | <math>-v\text{ }</math> | ||
+ | makes with the positive | ||
+ | <math>x</math> | ||
+ | -axis. | ||
+ | |||
+ | |||
[[Image:4_3_3_d.gif|center]] | [[Image:4_3_3_d.gif|center]] | ||
+ | |||
+ | Angle | ||
+ | <math>v</math> | ||
+ | angle | ||
+ | <math>\pi -v</math> | ||
+ | |||
+ | |||
+ | Therefore, the angle | ||
+ | <math>{\pi }/{2}\;-v</math> | ||
+ | has a | ||
+ | <math>y</math> | ||
+ | -coordinate which is equal to the | ||
+ | <math>x</math> | ||
+ | -coordinate for the angle | ||
+ | <math>v</math>, i.e. | ||
+ | |||
+ | |||
+ | <math>\sin \left( {\pi }/{2}\;-v \right)=\cos v</math> | ||
+ | |||
+ | |||
+ | and from exercise c, we know that | ||
+ | <math>\cos v=\sqrt{1-a^{2}}</math> | ||
+ | |||
+ | |||
+ | |||
+ | <math>\sin \left( \frac{\pi }{2}-v \right)=\sqrt{1-a^{2}}</math> |
Revision as of 11:11, 29 September 2008
The expression for the angle
2−v
2
2
Angle
−v
Therefore, the angle
2−v
2−v
=cosv
and from exercise c, we know that
1−a2
2−v
=
1−a2