Category: Trigonometry

Question Number 138999 by bramlexs22 last updated on 21/Apr/21 $$\mathrm{The}\mathrm{number}\mathrm{of}\mathrm{solutions}$$$$\mathrm{of}\mathrm{equations}\sqrt{13-18\tan \mathrm{x}}=6\tan \mathrm{x}-3$$$$\mathrm{where}-2\pi <\mathrm{x}<2\pi \mathrm{is}$$ 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}} \…

Question Number 7683 by new phone last updated on 08/Sep/16 $$\mathrm{If}\sin \theta +2\cos \theta =1$$$$\mathrm{Prove}\mathrm{that}2\sin \theta -\cos \theta =2$$ Commented by sandy_suhendra last updated on 08/Sep/16 $${sin}\theta+^{} \mathrm{2}{cos}\theta=\mathrm{1} \…

Question Number 138725 by mathsuji last updated on 17/Apr/21 $$Solveforrealnumbers$$$$\frac{sin\left(sinx\right)}{sinx}+\frac{cos\left(cosx\right)}{cosx}=1$$ Answered by mr W last updated on 18/Apr/21 $$t=\sin x$$$$\mathrm{cos}\:{x}=\pm\sqrt{\mathrm{1}−{t}^{\mathrm{2}}…

Question Number 7514 by Tawakalitu. last updated on 01/Sep/16 Answered by Yozzia last updated on 01/Sep/16 $$sin\left(\pi cos\alpha \right)=cos\left(\pi sin\alpha \right).$$$$Usingsina=cos(\frac{\pi }{2}-a),weget$$$$cos(\frac{\pi }{2}-\pi cos\alpha )=cos\left(\pi sin\alpha \right)$$$$\Rightarrow \frac{\pi }{2}-\pi cos\alpha =2n\pi \pm \pi sin\alpha (n\in \mathbb{Z})$$$$\mp\pi{sin}\alpha−\pi{cos}\alpha=\mathrm{2}{n}\pi−\frac{\pi}{\mathrm{2}}…

Question Number 7392 by Tawakalitu. last updated on 26/Aug/16 $$\sqrt{x}+5+\sqrt{x}+5=tan\mathrm{\Theta }$$$$$$$$findthevalueof\mathrm{\Theta }$$ Commented by Yozzia last updated on 26/Aug/16 $${general}\:{solution},\:\Theta={n}\pi+{tan}^{−\mathrm{1}} \left(\mathrm{2}\sqrt{{x}}+\mathrm{10}\right),\:{n}\in\mathbb{Z}.…