User talk:GrigorIII


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

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