- #1
mnb96
- 715
- 5
Hello,
I was following the derivation of the solid angle of right rectangular pyramid that I found at http://www.slac.stanford.edu/~bgerke/notes/solid_angle.pdf" .
I don't quite understand the step between the 3rd to the 4th equation. In particular how the integral
[tex]\int_{\theta_-}^{\theta_+}\sin(\theta) d\theta[/tex]
becomes,
[tex]2 \cos|\theta_{\pm}|[/tex]
Where [tex]\theta_{\pm} = \cot^{-1} (\tan\left( \pm \alpha/2)cos\phi \right)[/tex]
According to my calculation it should be:
[tex]2 \left( 1 - \cos(\theta_+) \right)[/tex]
Where is my mistake?
I was following the derivation of the solid angle of right rectangular pyramid that I found at http://www.slac.stanford.edu/~bgerke/notes/solid_angle.pdf" .
I don't quite understand the step between the 3rd to the 4th equation. In particular how the integral
[tex]\int_{\theta_-}^{\theta_+}\sin(\theta) d\theta[/tex]
becomes,
[tex]2 \cos|\theta_{\pm}|[/tex]
Where [tex]\theta_{\pm} = \cot^{-1} (\tan\left( \pm \alpha/2)cos\phi \right)[/tex]
According to my calculation it should be:
[tex]2 \left( 1 - \cos(\theta_+) \right)[/tex]
Where is my mistake?
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