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Find-for-acute-sin-and-cos-in-terms-of-0-lt-k-lt-1-if-sin-1-cos-cos-1-sin-k-

Question Number 224886 by ajfour last updated on 09/Oct/25 $${Find}\:{for}\:{acute}\:\theta,\:\mathrm{sin}\:\theta\:{and}\:\mathrm{cos}\:\theta \\ $$$${in}\:{terms}\:{of}\:\mathrm{0}<{k}<\mathrm{1}, \\ $$$${if}\:\:\:\:\frac{\mathrm{sin}\:\theta\left(\mathrm{1}−\mathrm{cos}\:\theta\right)}{\mathrm{cos}\:\theta\left(\mathrm{1}−\mathrm{sin}\:\theta\right)}={k}. \\ $$ Commented by ajfour last updated on 09/Oct/25 https://youtu.be/0yTJet-ZrLw?si=eNV2L9JpjRiUepqX Commented…

vol-g-V-det-g-dx-1-dx-2-dx-3-parametric-Surface-S-u-v-w-R-3-R-3-S-r-rsin-cos-rsin-sin-rcos-find-metric-tensor-g-g-11-

Question Number 224883 by fkwow344 last updated on 09/Oct/25 $$\int\:\mathrm{vol}\left({g}^{\:} \right)=\int_{\:{V}} \:\sqrt{\mathrm{det}\:\boldsymbol{\mathrm{g}}_{\mu\nu} }\:\mathrm{d}{x}^{\mathrm{1}} \wedge\mathrm{d}{x}^{\mathrm{2}} \wedge\mathrm{d}{x}^{\mathrm{3}} \\ $$$$\mathrm{parametric}\:\mathrm{Surface}\: \\ $$$$\overset{\rightarrow} {\mathcal{S}}\left({u},{v},{w}\right);\mathbb{R}^{\mathrm{3}} \rightarrow\mathbb{R}^{\mathrm{3}} \\ $$$$\overset{\rightarrow} {\mathcal{S}}\left({r},\theta,\rho\right)\begin{cases}{{r}\mathrm{sin}\left(\theta\right)\mathrm{cos}\left(\rho\right)}\\{{r}\mathrm{sin}\left(\theta\right)\mathrm{sin}\left(\rho\right)}\\{{r}\mathrm{cos}\left(\theta\right)}\end{cases}\: \\…

A-homogeneous-rod-AB-of-length-L-1-8m-and-mass-M-is-pivoted-at-the-centre-O-in-such-a-way-that-it-can-rotate-freely-in-the-vertical-plane-The-rod-is-initially-in-the-horizontal-position-An-insect-S-

Question Number 224859 by fantastic last updated on 08/Oct/25 $${A}\:{homogeneous}\:{rod}\:{AB}\:{of}\:{length} \\ $$$${L}=\mathrm{1}.\mathrm{8}{m}\:{and}\:{mass}\:{M}\:{is}\:{pivoted} \\ $$$${at}\:{the}\:{centre}\:{O}\:{in}\:{such}\:{a}\:{way}\:{that} \\ $$$${it}\:{can}\:{rotate}\:{freely}\:{in}\:{the}\:{vertical}\:{plane}. \\ $$$$ \\ $$$${The}\:{rod}\:{is}\:{initially}\:{in}\:{the}\:{horizontal} \\ $$$${position}.{An}\:{insect}\:{S}\:\:{of}\:{the}\: \\ $$$${same}\:{mass}\:{M}\:{falls}\:{vertically} \\…

can-you-guys-explan-why-metric-tensor-g-0-Riemann-metric-tensor-R-0-

Question Number 224866 by fkwow344 last updated on 08/Oct/25 $$\mathrm{can}\:\mathrm{you}\:\mathrm{guys}\:\mathrm{explan}\:\mathrm{why} \\ $$$$\mathrm{metric}\:\mathrm{tensor}\:\mathrm{g}_{\mu\nu} =\mathrm{0}\:\:\rightarrow\:\mathrm{Riemann}\:\mathrm{metric}\:\mathrm{tensor}\:{R}_{\alpha\gamma\beta} ^{\delta} =\mathrm{0} \\ $$ Answered by MrAjder last updated on 18/Oct/25 Terms…

Question-224845

Question Number 224845 by Ernestolisboa last updated on 07/Oct/25 Commented by mr W last updated on 07/Oct/25 $${you}\:{seem}\:{not}\:{to}\:{know}\:{how}\:{to}\:{use}\:{this} \\ $$$${forum}\:{properly}.\:{please}\:{read}\: \\ $$$$“{Forum}\:{Help}''\:{on}\:{the}\:{top}\:{of}\:{the}\:{app} \\ $$$${for}\:{more}\:{instructions}. \\…