Category: Trigonometry

Question Number 15393 by Tinkutara last updated on 10/Jun/17 $$\mathrm{A}\mathrm{man}\mathrm{observes}\mathrm{that}\mathrm{when}\mathrm{he}\mathrm{moves}\mathrm{up}$$$$\mathrm{a}\mathrm{distance}c\mathrm{metres}\mathrm{on}\mathrm{a}\mathrm{slope},\mathrm{the}$$$$\mathrm{angle}\mathrm{of}\mathrm{depression}\mathrm{of}\mathrm{a}\mathrm{point}\mathrm{on}\mathrm{the}$$$$\mathrm{horizontal}\mathrm{plane}\mathrm{from}\mathrm{the}\mathrm{base}\mathrm{of}\mathrm{the}$$$$\mathrm{slope}\mathrm{is}30°,\mathrm{and}\mathrm{when}\mathrm{he}\mathrm{moves}\mathrm{up}$$$$\mathrm{further}\mathrm{a}\mathrm{distance}c\mathrm{metres},\mathrm{the}\mathrm{angle}\mathrm{of}$$$$\mathrm{depression}\mathrm{of}\mathrm{that}\mathrm{point}\mathrm{is}45°.\mathrm{The}$$$$\mathrm{angle}\:\mathrm{of}\:\mathrm{inclination}\:\mathrm{of}\:\mathrm{the}\:\mathrm{slope}\:\mathrm{with}\:\mathrm{the} \…

Question Number 80929 by mathocean1 last updated on 08/Feb/20 $$\mathrm{show}\mathrm{that}$$$$cos\frac{\pi }{7}\cos \frac{2\pi }{7}\cos \frac{4\pi }{7}=-\frac{1}{8}$$ Commented by jagoll last updated on 08/Feb/20 $$letx=\frac{\pi }{7}$$$$\mathrm{cos}\:{x}\mathrm{cos}\:\mathrm{2}{x}\mathrm{cos}\:\mathrm{4}{x}\:×\frac{\mathrm{2sin}\:{x}}{\mathrm{2sin}\:{x}}\:= \…

Question Number 80896 by mathocean1 last updated on 07/Feb/20 $$\alpha \mathrm{is}\mathrm{a}\mathrm{real}\in ]0;\frac{\pi }{2}[.\mathrm{we}\mathrm{give}\mathrm{this}$$$$\left({\mathrm{E}}_{\alpha }\right):2x^2-2x\sqrt{2}\left(cos\alpha \right)+\cos 2\alpha =0$$$$1.\mathrm{show}\mathrm{that}\mathrm{\Delta }={8\sin }^{2}x$$$$ishowedit.$$$$2.S\mathrm{olve}{\mathrm{E}}_{\alpha }\mathrm{in}\mathbb{R}.$$$$ \…

Question Number 15328 by tawa tawa last updated on 09/Jun/17 $$\mathrm{Prove}\mathrm{that}.$$$${\sec }^4\left(\mathrm{x}\right)-{\mathrm{cosec}}^4\left(\mathrm{x}\right)=\frac{{\sin }^2\left(\mathrm{x}\right)-{\cos }^2\left(\mathrm{x}\right)}{{\sec }^4\left(\mathrm{x}\right)}$$ Answered by RasheedSoomro last updated…

Question Number 15301 by Tinkutara last updated on 09/Jun/17 $$\mathrm{With}\mathrm{the}\mathrm{help}\mathrm{of}\mathrm{graph},\mathrm{find}\mathrm{the}$$$$\mathrm{solution}\mathrm{set}\mathrm{of}\mathrm{inequation}\tan x>-\sqrt{3}.$$ Answered by mrW1 last updated on 09/Jun/17 $$\mathrm{x}\in (\mathrm{n}\pi -\frac{\pi }{3},\mathrm{n}\pi +\frac{\pi }{2})\wedge \mathrm{n}\in \mathbb{Z}$$ Commented…