Category: Trigonometry

Question Number 14879 by Tinkutara last updated on 05/Jun/17 $$\mathrm{Find}\mathrm{the}\mathrm{value}\mathrm{of}x,\mathrm{satisfying}$$$${\sin }^{2}x+\sin x-2⩾0$$ Answered by ajfour last updated on 05/Jun/17 $$\left(\mathrm{sin}\:{x}+\frac{\mathrm{1}}{\mathrm{2}}\right)^{\mathrm{2}} =\mathrm{2}+\frac{\mathrm{1}}{\mathrm{4}}=\left(\frac{\mathrm{3}}{\mathrm{2}}\right)^{\mathrm{2}} \…

Question Number 14752 by Tinkutara last updated on 04/Jun/17 $$\mathrm{Find}\mathrm{ordered}\mathrm{pair}\mathrm{of}(x,y)\mathrm{given}x,y\in$$$$[0,2\pi ]\mathrm{if}{3}^{\sin x+\cos y}=1\mathrm{and}$$$$5^{{\sin }^{2}x+{\cos }^{2}y}=5$$ Commented by Tinkutara last updated…

Question Number 14633 by Tinkutara last updated on 03/Jun/17 $$\mathrm{Solve}\mathrm{the}\mathrm{equation}:$$$$(1-\tan \theta )(1+\sin 2\theta )=1+\tan \theta$$ Commented by myintkhaing last updated on 03/Jun/17 $$\frac{1-tan\theta }{1+tan\theta }(1+sin2\theta )=1$$$$\frac{{cos}\mathrm{2}\theta}{\mathrm{1}+{sin}\mathrm{2}\theta}\:\left(\mathrm{1}+{sin}\mathrm{2}\theta\right)\:=\:\mathrm{1} \…

Question Number 14591 by Tinkutara last updated on 02/Jun/17 Answered by prakash jain last updated on 02/Jun/17 $$\mathrm{For}x\in \mathbb{R}$$$${\mathrm{cosec}}^{2}x⩾1$$$$\mathrm{tan}^{\mathrm{100}} {x}\geqslant\mathrm{0} \…

Question Number 14590 by Tinkutara last updated on 02/Jun/17 Answered by mrW1 last updated on 03/Jun/17 $$\sin y⩾\sin x-\cos \alpha \cos x$$$$\sin y⩾\sqrt{1+{\cos }^2\alpha }\times (\frac{1}{\sqrt{1+{\cos }^2\alpha }}\times \sin x-\frac{\cos \alpha }{\sqrt{1+{\cos }^2\alpha }}\times \cos x)$$$$\mathrm{sin}\:{y}\geqslant\sqrt{\mathrm{1}+\mathrm{cos}^{\mathrm{2}} \:\alpha}\left(\mathrm{cos}\:\theta×\mathrm{sin}\:{x}−\mathrm{sin}\:\theta\:×\mathrm{cos}\:{x}\right)…