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Category: Trigonometry

3-sin-x-cos-x-3-cos-x-sin-x-0-

Question Number 139141 by bramlexs22 last updated on 23/Apr/21 $$\:\:\:\mathrm{3}^{\mathrm{sin}\:\mathrm{x}} \:\mathrm{cos}\:\mathrm{x}\:−\mathrm{3}^{\mathrm{cos}\:\mathrm{x}} \:\mathrm{sin}\:\mathrm{x}\:=\:\mathrm{0} \\ $$ Answered by phanphuoc last updated on 23/Apr/21 $$\frac{\mathrm{3}^{{sinx}} }{{sinx}}=\frac{\mathrm{3}^{{cosx}} }{{cosx}}\rightarrow{sinx}={cosx}\rightarrow{tgx}=\mathrm{1}\rightarrow{x}=\pi/\mathrm{4}+{k}\pi \\…

expressf-8cos-15sin-in-the-form-rcos-where-r-gt-0-and-is-a-positive-acute-angle-hence-find-the-general-solution-of-the-equation-80cos-150sin-13-the-maximum-and-minimum-value-

Question Number 73544 by Rio Michael last updated on 13/Nov/19 $${expressf}\left(\theta\right)=\:\mathrm{8}{cos}\theta\:−\mathrm{15}{sin}\theta\:{in}\:{the}\:{form} \\ $$$$\:{rcos}\left(\theta\:+\:\alpha\right),\:{where}\:{r}>\mathrm{0}\:{and}\:\alpha\:{is}\:{a}\:{positive}\:{acute}\:{angle} \\ $$$${hence} \\ $$$${find}\:{the}\:{general}\:{solution}\:{of}\:{the}\:{equation} \\ $$$$\:\:\mathrm{80}{cos}\:\theta\:−\mathrm{150}{sin}\theta\:=\:\mathrm{13} \\ $$$${the}\:{maximum}\:{and}\:{minimum}\:{value}\:{of}\:\:\frac{\mathrm{5}}{{f}\left(\theta\right)\:+\:\mathrm{3}} \\ $$ Answered by…

find-the-general-solution-of-sin4x-cos2x-0-

Question Number 73538 by Rio Michael last updated on 13/Nov/19 $${find}\:{the}\:{general}\:{solution}\:{of}\: \\ $$$$\:{sin}\mathrm{4}{x}\:+\:{cos}\mathrm{2}{x}\:=\:\mathrm{0} \\ $$ Answered by ajfour last updated on 13/Nov/19 $$\mathrm{cos}\:\mathrm{2}{x}\left(\mathrm{2sin}\:\mathrm{2}{x}+\mathrm{1}\right)=\mathrm{0} \\ $$$$\Rightarrow\:\:\mathrm{2}{x}=\left(\mathrm{2}{n}+\mathrm{1}\right)\frac{\pi}{\mathrm{2}}\:\:\:{or}…

Question-139075

Question Number 139075 by bramlexs22 last updated on 22/Apr/21 Answered by mr W last updated on 22/Apr/21 $$\mathrm{tan}\:\alpha=\frac{{x}}{\mathrm{144}} \\ $$$$\mathrm{tan}\:\beta=\frac{{x}}{\mathrm{144}+\mathrm{81}}=\frac{{x}}{\mathrm{225}} \\ $$$$\mathrm{tan}\:\gamma=\frac{{x}}{\mathrm{225}+\mathrm{99}}=\frac{{x}}{\mathrm{324}} \\ $$$$\mathrm{tan}\:\gamma=\mathrm{tan}\:\left(\mathrm{90}°−\alpha−\beta\right)=\frac{\mathrm{1}}{\mathrm{tan}\:\left(\alpha+\beta\right)} \\…

The-number-of-solutions-of-equations-13-18tan-x-6tan-x-3-where-2pi-lt-x-lt-2pi-is-

Question Number 138999 by bramlexs22 last updated on 21/Apr/21 $$\mathrm{The}\:\mathrm{number}\:\mathrm{of}\:\mathrm{solutions} \\ $$$$\mathrm{of}\:\mathrm{equations}\:\sqrt{\mathrm{13}−\mathrm{18tan}\:\mathrm{x}}\:=\:\mathrm{6tan}\:\mathrm{x}−\mathrm{3} \\ $$$$\mathrm{where}\:−\mathrm{2}\pi<\mathrm{x}<\mathrm{2}\pi\:\mathrm{is} \\ $$ Answered by EDWIN88 last updated on 21/Apr/21 $$\left(\mathrm{1}\right)\:\mathrm{13}−\mathrm{18tan}\:\mathrm{x}\geqslant\mathrm{0}\:;\:\mathrm{tan}\:\mathrm{x}\leqslant\frac{\mathrm{13}}{\mathrm{18}} \\…

tan-16-4-2-2-2-1-

Question Number 7841 by ankursharma532 last updated on 19/Sep/16 $${tan}\Pi/\mathrm{16}=\sqrt{\mathrm{4}+\mathrm{2}\sqrt{\mathrm{2}}\:}\:−\:\left(\sqrt{\mathrm{2}}\:+\mathrm{1}\right) \\ $$ Commented by Yozzia last updated on 19/Sep/16 $${tan}\mathrm{4}{x}=\frac{\mathrm{2}{tan}\mathrm{2}{x}}{\mathrm{1}−{tan}^{\mathrm{2}} \mathrm{2}{x}} \\ $$$${Let}\:{x}=\pi/\mathrm{16}\Rightarrow{tan}\mathrm{4}{x}={tan}\frac{\pi}{\mathrm{4}}=\mathrm{1} \\ $$$$\therefore\mathrm{2}{tan}\mathrm{2}{x}=\mathrm{1}−{tan}^{\mathrm{2}}…