Category: Trigonometry

Question Number 14470 by Tinkutara last updated on 01/Jun/17 $$\mathrm{Find}\mathrm{the}\mathrm{number}\mathrm{of}\mathrm{solution}\left(\mathrm{s}\right)\mathrm{of}$$$$x^2+x+\sin x=0,x\in [0,\pi ]$$ Commented by mrW1 last updated on 01/Jun/17 $$sincex\in [0,\pi ]$$$${x}^{\mathrm{2}}…

Question Number 14438 by ajfour last updated on 31/May/17 $$\mathit{x}=\frac{2\mathit{a}}{\sqrt{3}}\sin \mathit{\theta },\mathit{y}=\frac{2\mathit{b}}{\sqrt{3}}\sin \mathit{\varphi },and$$$$\mathit{z}=\frac{2\mathit{c}}{\sqrt{3}}\sin \mathit{\psi };where\mathit{a},\mathit{b},and\mathit{c}$$$$aresidesof△ABCsuchthat$$$$\mathit{\varphi }-\mathit{\psi }+\frac{\pi }{3}=\mathrm{\angle }\mathit{A},$$$$\mathit{\psi }-\mathit{\theta }+\frac{\pi }{3}=\mathrm{\angle }\mathit{B},and$$$$\mathit{\theta }-\mathit{\psi }+\frac{\pi }{3}=\mathrm{\angle }\mathit{C}.$$$$Findatleastonefeasible$$$${solution}\:{set}\:{of}\:\boldsymbol{\theta},\boldsymbol{\phi},\:{and}\:\boldsymbol{\psi}\:{in} \…

Question Number 14330 by myintkhaing last updated on 01/Jun/17 $$tan\theta +tan2\theta =tan3\theta$$$$\frac{tan\theta +tan2\theta }{1-tan\theta tan2\theta }(1-tan\theta tan2\theta )=tan3\theta$$$$tan3\theta (1-tan\theta tan2\theta )=tan3\theta$$$$tan\theta tan2\theta tan3\theta 0$$$$3\theta =k\pi ,wherek=0,1,2,3,\dots$$$$\theta =\frac{k\pi }{3}$$$$tan\theta =0ortan2\theta =0ortan3\theta =0$$$$\theta={m}\pi,\:{where}\:{m}=\mathrm{0},\mathrm{1},\mathrm{2},\mathrm{3},… \…

Question Number 14268 by Tinkutara last updated on 30/May/17 $$\mathrm{If}\tan \theta +\tan 2\theta =\tan 3\theta ,\mathrm{find}\mathrm{the}$$$$\mathrm{exhaustive}\mathrm{set}\mathrm{of}\mathrm{values}\mathrm{of}\theta \mathrm{satisfying}$$$$\mathrm{the}\mathrm{given}\mathrm{equation}.$$ Answered by linkelly0615 last updated on 30/May/17 $$\because{tan}\mathrm{3}\theta=\frac{{tan}\theta+{tan}\mathrm{2}\theta}{\mathrm{1}−{tan}\theta{tan}\mathrm{2}\theta}={tan}\theta+{tan}\mathrm{2}\theta \…

Question Number 14267 by Tinkutara last updated on 30/May/17 $$\mathrm{If}{\sin }^{3}x+{\cos }^{3}x+3\sin x\cos x-1=0,$$$$\mathrm{then}\mathrm{find}x.$$ Answered by linkelly0615 last updated on 30/May/17 $${set} \…