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Category: Trigonometry

sin-A-sin-2A-sin-3A-sin-nA-

Question Number 114627 by john santu last updated on 20/Sep/20 $$\mathrm{sin}\:{A}+\mathrm{sin}\:\mathrm{2}{A}+\mathrm{sin}\:\mathrm{3}{A}+…+\mathrm{sin}\:{nA}\:=?? \\ $$ Answered by mathmax by abdo last updated on 20/Sep/20 $$\mathrm{let}\:\mathrm{S}_{\mathrm{n}} \left(\mathrm{x}\right)\:=\mathrm{sinx}\:+\mathrm{sin}\left(\mathrm{2x}\right)+…+\mathrm{sin}\left(\mathrm{nx}\right)=\sum_{\mathrm{k}=\mathrm{0}} ^{\mathrm{n}}…

solve-for-0-2pi-the-equation-cos-pi-3-1-2-

Question Number 49064 by Rio Michael last updated on 02/Dec/18 $${solve}\:{for}\:\mathrm{0}°\leqslant\theta\leqslant\mathrm{2}\pi\:{the}\:{equation} \\ $$$${cos}\left(\theta\:+\:\frac{\pi}{\mathrm{3}}\right)\:=\:\frac{\mathrm{1}}{\mathrm{2}} \\ $$ Answered by hknkrc46 last updated on 02/Dec/18 $$\mathrm{cos}\:\left(\theta+\frac{\pi}{\mathrm{3}}\right)=\mathrm{cos}\:\left(\frac{\pi}{\mathrm{3}}\right) \\ $$$$\theta+\frac{\pi}{\mathrm{3}}=\frac{\pi}{\mathrm{3}}+\mathrm{2}\pi{k}\:\vee\:−\left(\theta+\frac{\pi}{\mathrm{3}}\right)=\frac{\pi}{\mathrm{3}}+\mathrm{2}\pi{k}\:\left({k}\in\mathbb{Z}\right)…

4-2cos-2pi-13x-9-2-5sin-pi-13x-9-2-x-

Question Number 180025 by cortano1 last updated on 06/Nov/22 $$\:\:\:\:\:\:\:\mathrm{4}−\mathrm{2cos}\:\left(\mathrm{2}\pi\left(\mathrm{13x}+\mathrm{9}\right)^{\mathrm{2}} \right)=\:\mathrm{5sin}\:\left(\pi\left(\mathrm{13x}+\mathrm{9}\right)^{\mathrm{2}} \right) \\ $$$$\:\mathrm{x}=? \\ $$ Answered by Frix last updated on 06/Nov/22 $$\mathrm{4}−\mathrm{2cos}\:\mathrm{2}\alpha\:=\mathrm{5sin}\:\alpha \\…

sin-2-3pi-7-sin-2-2pi-7-sin-3pi-7-sin-2pi-7-1-2sin-5pi-14-

Question Number 180018 by cortano1 last updated on 06/Nov/22 $$\:\:\frac{\mathrm{sin}\:^{\mathrm{2}} \left(\frac{\mathrm{3}\pi}{\mathrm{7}}\right)}{\mathrm{sin}\:^{\mathrm{2}} \left(\frac{\mathrm{2}\pi}{\mathrm{7}}\right)}\:+\:\frac{\mathrm{sin}\:\left(\frac{\mathrm{3}\pi}{\mathrm{7}}\right)}{\mathrm{sin}\:\left(\frac{\mathrm{2}\pi}{\mathrm{7}}\right)}\:+\mathrm{1}−\mathrm{2sin}\:\left(\frac{\mathrm{5}\pi}{\mathrm{14}}\right)\:=? \\ $$ Commented by Frix last updated on 06/Nov/22 $$\mathrm{2} \\ $$ Terms…