Category: Trigonometry

Question Number 63682 by Annmuema last updated on 07/Jul/19 $$givendiameter25mm$$$$halfofthedrillpointangle=60$$$$cuttingvelocity=44000mm/minute$$$$length=60mm$$$$feedrate=0.25mm/revolution$$$$determinethetimeneededtodrillathroughhole$$ Terms of Service…

Question Number 63643 by vajpaithegrate@gmail.com last updated on 06/Jul/19 $$\mathrm{P}(\alpha ,\beta )\mathrm{Q}(\gamma ,\delta )\mathrm{are}\mathrm{two}\mathrm{points}\mathrm{lie}\mathrm{on}\mathrm{curve}$$$${\tan }^2(\mathrm{x}+\mathrm{y})+{\cos }^2(\mathrm{x}+\mathrm{y})+{\mathrm{y}}^2+2\mathrm{y}=0\mathrm{on}$$$$\mathrm{XY}\mathrm{plane}.\mathrm{If}\mathrm{d}=\mathrm{PQ}\mathrm{then}\cos \mathrm{d}=$$$$\mathrm{ans}:\pm 2\mathrm{n}\pi ,\mathrm{n}\in \mathrm{N}$$ Answered by MJS last…

Question Number 129070 by benjo_mathlover last updated on 12/Jan/21 $$\mathrm{Solve}2\cos \mathrm{x}\cos 2\mathrm{x}=\cos (\frac{\pi }{3}-3\mathrm{x})$$ Answered by liberty last updated on 12/Jan/21 $$\iff 2\cos \mathrm{x}\cos 2\mathrm{x}=\cos (\frac{\pi }{3}-3\mathrm{x})$$$$\iff \cos 3\mathrm{x}+\cos \mathrm{x}=\frac{1}{2}\cos 3\mathrm{x}+\frac{\sqrt{3}}{2}\sin 3\mathrm{x}$$$$\:\Leftrightarrow\:\mathrm{cos}\:\mathrm{x}\:=\:\frac{\sqrt{\mathrm{3}}}{\mathrm{2}}\:\mathrm{sin}\:\mathrm{3x}−\frac{\mathrm{1}}{\mathrm{2}}\mathrm{cos}\:\mathrm{3x}\: \…

Question Number 129051 by oustmuchiya@gmail.com last updated on 12/Jan/21 $$provethat\frac{1+\mathit{s}\mathit{i}\mathit{n}\mathit{x}}{\mathit{s}\mathit{i}\mathit{n}\mathit{x}\mathit{c}\mathit{o}\mathit{s}\mathit{x}}=$$$$\mathit{t}\mathit{a}\mathit{n}\mathit{x}+\mathit{c}\mathit{o}\mathit{t}\mathit{x}+\mathit{s}\mathit{e}\mathit{c}\mathit{x}\mathit{h}\mathit{e}\mathit{n}\mathit{c}\mathit{e}$$$$\mathit{d}\mathit{i}\mathit{f}\mathit{f}\mathit{e}\mathit{r}\mathit{e}\mathit{n}\mathit{t}\mathit{i}\mathit{a}\mathit{t}\mathit{e}\mathit{t}\mathit{h}\mathit{e}\mathit{f}\mathit{u}\mathit{n}\mathit{c}\mathit{t}\mathit{i}\mathit{o}\mathit{n}$$ Answered by mindispower last updated on 12/Jan/21 $$\mathrm{1}={cos}^{\mathrm{2}} \left({x}\right)+{sin}^{\mathrm{2}}…

Question Number 63466 by vajpaithegrate@gmail.com last updated on 04/Jul/19 $$\mathrm{If}\mathrm{A}={\sin }^{28}\theta +{\cos }^{36}\theta \mathrm{then}$$$$\mathrm{Ans}:0<\mathrm{A}⩽1$$ Commented by MJS last updated on 05/Jul/19 $$\mathrm{0}\leqslant\mathrm{cos}^{\mathrm{36}} \:\theta\:\leqslant\mathrm{1}…