Category: Trigonometry

Question Number 144452 by imjagoll last updated on 25/Jun/21 $$\mathrm{Find}\mathrm{minimum}\mathrm{value}\mathrm{of}$$$$\mathrm{f}\left(\mathrm{x}\right)=\sin (\mathrm{x}+3)-\sin (\mathrm{x}+1)-2\cos (\mathrm{x}+2)$$$$\mathrm{where}\mathrm{x}ϵ\mathrm{R}$$ Answered by EDWIN88 last updated on 25/Jun/21 $$\:\mathrm{f}\left(\mathrm{x}\right)=\mathrm{sin}\:\left(\mathrm{x}+\mathrm{3}\right)−\mathrm{sin}\:\left(\mathrm{x}+\mathrm{1}\right)−\mathrm{2cos}\:\left(\mathrm{x}+\mathrm{2}\right) \…

Question Number 13329 by chux last updated on 18/May/17 $$\mathrm{A}\mathrm{surveyor}\mathrm{standing}\mathrm{at}\mathrm{a}\mathrm{point}\mathrm{X},$$$$\mathrm{sites}\mathrm{a}\mathrm{post}\mathrm{Y}\mathrm{due}\mathrm{east}\mathrm{of}\mathrm{him}\mathrm{and}$$$$\mathrm{a}\mathrm{tower}\mathrm{Z}\mathrm{of}\mathrm{a}\mathrm{building}\mathrm{on}\mathrm{a}$$$$\mathrm{bearing}\mathrm{of}046°.\mathrm{After}\mathrm{walking}\mathrm{to}\mathrm{a}$$$$\mathrm{point}\mathrm{W},\mathrm{a}\mathrm{distance}\mathrm{of}180\mathrm{m}\mathrm{in}\mathrm{the}$$$$\mathrm{south}-\mathrm{east}\mathrm{direction}\mathrm{he}\mathrm{observes}$$$$\mathrm{the}\mathrm{bearing}\mathrm{of}\mathrm{Z}\mathrm{and}\mathrm{Y}\mathrm{to}\mathrm{be}337°$$$$\mathrm{and}\:\mathrm{50}°\:\mathrm{respectively}. \…

Question Number 78815 by mathocean1 last updated on 20/Jan/20 $$\mathrm{show}\mathrm{that}$$$$\sin \frac{2\pi }{5}=\sin \frac{3\pi }{5}$$ Answered by mind is power last updated on 20/Jan/20 $$\frac{\mathrm{3}\pi}{\mathrm{5}}=\pi−\frac{\mathrm{2}\pi}{\mathrm{5}}\:\:\: \…

Question Number 144329 by gsk2684 last updated on 24/Jun/21 $$\mathrm{find}\mathrm{the}\mathrm{number}\mathrm{of}\mathrm{solutions}$$$$\mathrm{of}\sqrt{6-\cos \mathrm{x}+{7\sin }^2\mathrm{x}}+\cos \mathrm{x}=0$$ Commented by MJS_new last updated on 25/Jun/21 $$\mathrm{let}c=\cos x\Rightarrow -1⩽c⩽1$$$$\sqrt{\mathrm{13}−{c}−\mathrm{7}{c}^{\mathrm{2}}…

Question Number 78785 by jagoll last updated on 20/Jan/20 $$$$$$$$$${(1+\sin \frac{\pi }{7})}^{3-\cos 2\mathrm{x}}={(\sin \frac{\pi }{14}+\cos \frac{\pi }{14})}^{10\sin \mathrm{x}}$$$$\mathrm{find}\mathrm{solution}$$ Answered by john santu last updated…