Identidade trigonométrica: diferenças entre revisões

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|<math>\begin{align}&\sen \frac{\theta}{2} = \sgn \!\! \left( \!\! 2 \pi \! - \! \theta \! + \! 4 \pi \! \left\lfloor \! \frac{\theta}{4\pi} \! \right\rfloor \! \right) \!\! \sqrt{\frac{1 \! - \! \cos \theta}{2}} \\ \\

|<math>\begin{align}&\cos \frac{\theta}{2} = \sgn \!\! \left(\!\! \pi \! + \! \theta \! + \! 4 \pi \! \left\lfloor \! \frac{\pi \! - \! \theta}{4\pi} \! \right\rfloor \! \right) \!\! \sqrt{\frac{1 + \cos\theta}{2}} \\ \\

|<math>\begin{align} \tan \frac{\theta}{2} &= \csc \theta - \cot \theta \\ &= \pm\, \sqrt{1 - \cos \theta \over 1 + \cos \theta} \\[8pt] &= \frac{\sen \theta}{1 + \cos \theta} \\[8pt] &= \frac{1-\cos \theta}{\sen \theta} \\[10pt]

\tan\frac{\eta+\theta}{2} & = \frac{\sen\eta+\sen\theta}{\cos\eta+\cos\theta} \\[8pt]