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if-tan-r-s-and-sin-s-r-show-that-cos-r-2-s-

Question Number 33466 by mondodotto@gmail.com last updated on 17/Apr/18 $$\:\boldsymbol{\mathrm{if}}\:\boldsymbol{\mathrm{tan}\beta}=\frac{\boldsymbol{\mathrm{r}}}{\:\sqrt{\boldsymbol{\mathrm{s}}}}\:\boldsymbol{\mathrm{and}}\:\boldsymbol{\mathrm{sin}\beta}=\frac{\sqrt{\boldsymbol{\mathrm{s}}}}{\boldsymbol{\mathrm{r}}} \\ $$$$\:\boldsymbol{\mathrm{show}}\:\boldsymbol{\mathrm{that}}\:\boldsymbol{\mathrm{cos}\beta}=\sqrt{\boldsymbol{\mathrm{r}}^{\mathrm{2}} +\boldsymbol{\mathrm{s}}} \\ $$ Commented by MJS last updated on 17/Apr/18 $$\mathrm{cos}\:\beta=\sqrt{\mathrm{1}−\mathrm{sin}^{\mathrm{2}} \:\beta}=\frac{\sqrt{{r}^{\mathrm{2}} −{s}}}{\mid{r}\mid}…

A-circle-is-drawn-with-center-0-1-and-radius-1-A-line-OAB-is-drawn-making-an-angle-with-the-x-axis-to-cut-the-circle-at-A-and-the-tangent-to-the-circle-at-0-2-at-B-Lines-are-now-drawn-through

Question Number 164520 by ZiYangLee last updated on 18/Jan/22 $$\mathrm{A}\:\mathrm{circle}\:\mathrm{is}\:\mathrm{drawn}\:\mathrm{with}\:\mathrm{center}\:\left(\mathrm{0},\mathrm{1}\right)\:\mathrm{and}\:\mathrm{radius}\:\mathrm{1}. \\ $$$$\mathrm{A}\:\mathrm{line}\:\mathrm{OAB}\:\mathrm{is}\:\mathrm{drawn},\:\mathrm{making}\:\mathrm{an}\:\mathrm{angle}\:\theta\:\mathrm{with}\:\mathrm{the} \\ $$$${x}-\mathrm{axis}\:\mathrm{to}\:\mathrm{cut}\:\mathrm{the}\:\mathrm{circle}\:\mathrm{at}\:{A}\:\mathrm{and}\:\mathrm{the}\:\mathrm{tangent}\:\mathrm{to}\:\mathrm{the} \\ $$$$\mathrm{circle}\:\mathrm{at}\:\left(\mathrm{0},\mathrm{2}\right)\:\mathrm{at}\:{B}.\:\mathrm{Lines}\:\mathrm{are}\:\mathrm{now}\:\mathrm{drawn}\:\mathrm{through} \\ $$$${A}\:\mathrm{and}\:{B}\:\:\mathrm{parallel}\:\mathrm{to}\:\mathrm{the}\:{x}-\:\mathrm{and}\:{y}-\mathrm{axes}\:\mathrm{respectively} \\ $$$$\mathrm{to}\:\mathrm{intersect}\:\mathrm{at}\:{P}.\:\:\:\mathrm{Prove}\:\mathrm{that} \\ $$$$\left(\mathrm{i}\right)\:\mathrm{OA}=\mathrm{2}\:\mathrm{sin}\:\theta\:\:\:\:\:\mathrm{and}\: \\ $$$$\left(\mathrm{ii}\right)\mathrm{the}\:\mathrm{coordinates}\:\mathrm{of}\:{P}\:\mathrm{are}\:\left(\mathrm{2}\:\mathrm{cot}\:\theta,\:\mathrm{2}\:\mathrm{sin}^{\mathrm{2}} \theta\right)…

Question-164507

Question Number 164507 by mathlove last updated on 18/Jan/22 Commented by mathlove last updated on 18/Jan/22 $$\mathrm{tan}\theta=\frac{\mathrm{1}}{\mathrm{3}}\:\:{and}\:\:\:\mathrm{tan}\:\beta=\frac{\mathrm{3}}{\mathrm{4}} \\ $$$${faind}\:\:{a}\:\:{and}\:\:\:{b} \\ $$ Commented by mr W…

solve-2-6-x-1-9-x-2-dx-0-1-x-1-x-1-x-dx-n-1-1-n-j-1-n-3-2-j-2n-1-n-

Question Number 98967 by  M±th+et+s last updated on 17/Jun/20 $${solve}: \\ $$$$\left(\frac{\int_{\mathrm{2}} ^{\mathrm{6}} {x}\sqrt{\mathrm{1}+\mathrm{9}\lfloor{x}\rfloor^{\mathrm{2}} }{dx}}{\int_{\mathrm{0}} ^{\mathrm{1}} {x}\left\{\frac{\mathrm{1}}{{x}}\right\}\lceil\frac{\mathrm{1}}{{x}}\rceil{dx}}\right)\left(\underset{{n}\geqslant\mathrm{1}} {\sum}\left(−\mathrm{1}\right)^{{n}} \frac{\prod_{{j}=\mathrm{1}} ^{{n}} \left(\frac{\mathrm{3}}{\mathrm{2}}−{j}\right)}{\left(\mathrm{2}{n}+\mathrm{1}\right){n}!}\right) \\ $$ Answered by…

please-is-there-any-general-way-for-calculating-the-error-or-uncertainty-in-g-when-m-4pi-2-g-where-m-slope-and-g-acceleration-due-to-gravity-please-help-

Question Number 33410 by NECx last updated on 15/Apr/18 $${please}\:{is}\:{there}\:{any}\:{general}\:{way}\:{for} \\ $$$${calculating}\:{the}\:{error}\:{or}\:{uncertainty} \\ $$$${in}\:{g}\:{when} \\ $$$$ \\ $$$$\:\:\:\:\:\:\:{m}=\frac{\mathrm{4}\pi^{\mathrm{2}} }{{g}}\:{where}\:{m}={slope}\:{and} \\ $$$${g}={acceleration}\:{due}\:{to}\:{gravity} \\ $$$$ \\ $$$$…

Given-u-0-C-u-n-1-u-n-u-n-2-n-N-where-u-n-n-N-is-a-complex-sequence-Determinate-the-sequence-Im-u-n-n-N-and-calculate-its-limit-NB-Im-u-n-is-the-co

Question Number 164478 by mathocean1 last updated on 17/Jan/22 $${Given}\:\begin{cases}{{u}_{\mathrm{0}} =\alpha\:\in\:\mathbb{C}}\\{{u}_{{n}+\mathrm{1}} =\frac{{u}_{{n}} +\mid{u}_{{n}} \mid}{\mathrm{2}}}\end{cases}\:;\:{n}\in\:\mathbb{N} \\ $$$${where}\:\left({u}_{{n}} \right)\:_{{n}\in\mathbb{N}} \:{is}\:{a}\:{complex}\:{sequence}. \\ $$$${Determinate}\:{the}\:{sequence}\:\left({Im}\left({u}_{{n}} \right)\right)\:_{{n}\in\mathbb{N}} \\ $$$${and}\:{calculate}\:{its}\:{limit}. \\ $$$${NB}:\:{Im}\left({u}_{{n}}…