T-Formula (1 Viewer)

nrumble42 · Jan 18, 2017

Hey guys!
How do I write sin theta/2 and cost theta/2 using the T formulas??

Any help would be great

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InteGrand · Jan 18, 2017

nrumble42 said:
Hey guys!
How do I write sin theta/2 and cost theta/2 using the T formulas??

Any help would be great

Sent from my SM-G920I using Tapatalk

$\noindent Do you want $\sin \theta$ and $\cos \theta$ in terms of $T\equiv \tan \theta$? For $\theta \in \left(-\frac{\pi}{2},\frac{\pi}{2}\right)$, these are$

$\sin \theta = \frac{T}{\sqrt{1+T^{2}}}, \quad \cos \theta = \frac{1}{\sqrt{1+T^{2}}}.$

$\noindent Also, $\mathrm{d}\theta = \frac{1}{1+T^{2}}\,\mathrm{d}T$ (useful if integrating).$

InteGrand · Jan 18, 2017

T-Formula (1 Viewer)

nrumble42

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InteGrand

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InteGrand

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