User talk:GrigorIII

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rcos(3x+\theta)\,
=r(cos3xcos\theta-sin3xsin\theta)\,
=rcos3xcos\theta-rsin3xsin\theta\,
=\begin{cases} rcos\theta=5 \\-rsin\theta=-6 \end{cases} \,
=\begin{cases} rcos\theta=5 &--(i) \\rsin\theta=6 &--(ii) \end{cases} \,
i^2+ii^2=r^2cos^2\theta+r^2sin^2\theta=5^2+6^2\,
r^2=61 \,
r=\sqrt{61}
\frac{ii}{i}=\frac{rsin\theta}{rcos\theta}=\frac{6}{5}
tan\theta=\frac{6}{5}
\theta\approx50.2^\circ
\mbox{so }5cos3x-6sin3x\approx \sqrt{61}cos(3x+50.2^\circ)
5cos3x-6sin3x=4 \,
\sqrt{61}cos(3x+50.2^\circ)=4
cos(3x+50.2^\circ)\approx cos59.2^\circ
3x+50.2^\circ\approx360^\circ n \pm 59.2^\circ
3x=360^\circ n + 59.2^\circ-50.2^\circ \mbox{ or } 3x=360^\circ n -59.2^\circ-50.2^\circ
x=120^\circ n +3^\circ \mbox{ or } x=120^\circ n-\frac{109.4\circ}{3}
\mbox{where n is integer}\,

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Hi there. May I ask what you are trying to achieve with the above template? --TheParanoidOne 20:22, 21 August 2006 (UTC)

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