Resolver S=2cos(2/3t-pi/9) | Microsoften solucionagailu matematikoa

Ebatzi: S (complex solution)

S=e^{\frac{2it}{3}-\frac{\pi i}{9}}+e^{-\frac{2it}{3}+\frac{\pi i}{9}}

Ebatzi: t (complex solution)

t=\frac{-9i\ln(\frac{\sqrt{S^{2}-4}+S}{2})+\pi }{6}+3\pi n_{1}\text{, }n_{1}\in \mathrm{Z}

t=\frac{-9i\ln(\frac{-\sqrt{S^{2}-4}+S}{2})+\pi }{6}+3\pi n_{2}\text{, }n_{2}\in \mathrm{Z}

Ebatzi: S

S=2\cos(\frac{6t-\pi }{9})

Ebatzi: t

t=\frac{-9\arccos(\frac{S}{2})+18\pi n_{1}+\pi }{6}\text{, }n_{1}\in \mathrm{Z}

t=\frac{9\arccos(\frac{S}{2})+18\pi n_{2}+\pi }{6}\text{, }n_{2}\in \mathrm{Z}

Azterketa

Trigonometry

antzeko 5 arazoen antzekoak:

S = 2 \cos ( \frac { 2 } { 3 } t - \frac { \pi } { 9 } )

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