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Category: Trigonometry

Solve-for-x-tan-x-tan-2x-tan-3x-0-Some-one-had-posted-this-question-and-I-had-answered-it-but-then-thread-was-deleted-I-think-that-the-question-is-not-importanceless-so-I-hav-reposted-it-

Question Number 1890 by Rasheed Soomro last updated on 21/Oct/15 $${Solve}\:{for}\:{x} \\ $$$$\:\:\:\:\:\:{tan}\:{x}\:+{tan}\:\mathrm{2}{x}\:−{tan}\:\mathrm{3}{x}\:=\mathrm{0} \\ $$$${Some}\:{one}\:{had}\:{posted}\:{this}\:{question}\:{and}\:{I}\:{had}\:{answered}\:{it} \\ $$$${but}\:{then}\:{thread}\:{was}\:{deleted}! \\ $$$${I}\:{think}\:{that}\:{the}\:{question}\:{is}\:{not}\:{importanceless}\:,\:{so}\:{I}\:{hav} \\ $$$${reposted}\:{it}. \\ $$ Commented by…

Question-67396

Question Number 67396 by Cmr 237 last updated on 26/Aug/19 Commented by mathmax by abdo last updated on 26/Aug/19 $${let}\:{P}\left({z}\right)\:=\:{z}^{\mathrm{2}{n}} \:+\mathrm{1}\:{let}\:{determine}\:{the}\:{roots}\:{of}\:{P}\left({z}\right) \\ $$$${P}\left({z}\right)=\mathrm{0}\:\Leftrightarrow\:{z}^{\mathrm{2}{n}} \:=−\mathrm{1}\:\:\Leftrightarrow\:\:{z}^{\mathrm{2}{n}} ={e}^{{i}\left(\mathrm{2}{k}+\mathrm{1}\right)\pi}…

Show-that-given-4cos-pi-3-2-3-sin-pi-3-5-then-pi-3cos-1-5-28-3tan-1-3-2-

Question Number 1830 by 112358 last updated on 10/Oct/15 $${Show}\:{that}\:{given} \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\mathrm{4}{cos}\frac{\pi}{\mathrm{3}}+\mathrm{2}\sqrt{\mathrm{3}}{sin}\frac{\pi}{\mathrm{3}}=\mathrm{5} \\ $$$${then} \\ $$$$\:\:\:\:\:\:\:\pi=\mathrm{3}{cos}^{−\mathrm{1}} \left(\frac{\mathrm{5}}{\:\sqrt{\mathrm{28}}}\right)+\mathrm{3}{tan}^{−\mathrm{1}} \left(\frac{\sqrt{\mathrm{3}}}{\mathrm{2}}\right)\:. \\ $$ Answered by Rasheed Soomro last…

Find-the-period-of-f-x-where-f-x-cos-2x-pi-3-sin-3x-2-pi-4-How-may-one-find-the-period-of-the-following-functions-if-x-has-period-m-and-x-has-period-n-1-f-1-x-x-x-2-f-2-x

Question Number 1812 by 112358 last updated on 04/Oct/15 $${Find}\:{the}\:{period}\:{of}\:{f}\left({x}\right)\:{where} \\ $$$${f}\left({x}\right)={cos}\left(\mathrm{2}{x}+\frac{\pi}{\mathrm{3}}\right)+{sin}\left(\frac{\mathrm{3}{x}}{\mathrm{2}}−\frac{\pi}{\mathrm{4}}\right). \\ $$$${How}\:{may}\:{one}\:{find}\:{the}\:{period} \\ $$$${of}\:{the}\:{following}\:{functions} \\ $$$${if}\:\psi\left({x}\right)\:{has}\:{period}\:{m}\:{and}\:\gamma\left({x}\right) \\ $$$${has}\:{period}\:{n}? \\ $$$$\left(\mathrm{1}\right)\:{f}_{\mathrm{1}} \left({x}\right)=\psi\left({x}\right)\gamma\left({x}\right) \\ $$$$\left(\mathrm{2}\right)\:{f}_{\mathrm{2}}…

Prove-sin-a-sin-a-14pi-3-sin-a-8pi-3-0-

Question Number 1808 by alib last updated on 04/Oct/15 $$\boldsymbol{\mathcal{P}}{rove}\:\:\mathrm{sin}\:\left({a}\right)+\mathrm{sin}\:\left({a}+\frac{\mathrm{14}\pi}{\mathrm{3}}\right)+\mathrm{sin}\:\left({a}−\frac{\mathrm{8}\pi}{\mathrm{3}}\right)=\mathrm{0}/ \\ $$$$ \\ $$ Answered by 112358 last updated on 05/Oct/15 $${Using}\:{the}\:{compound}\:{angle}\:{formula} \\ $$$${sin}\left({x}\pm{y}\right)={sinxcosy}\pm{cosxsiny}\:{we}\:{get} \\…

3sinx-5cosx-5-then-prove-that-5sinx-3cox-3-

Question Number 67345 by Aditya789 last updated on 26/Aug/19 $$\mathrm{3}{sinx}+\mathrm{5}{cosx}=\mathrm{5}\:{then}\:{prove}\:{that}\: \\ $$$$\mathrm{5}{sinx}−\mathrm{3}{cox}=\:+\mathrm{3} \\ $$ Answered by $@ty@m123 last updated on 26/Aug/19 $$\frac{\mathrm{3}}{\mathrm{5}}\mathrm{sin}\:{x}+\mathrm{cos}\:{x}=\mathrm{1} \\ $$$$\frac{\mathrm{1}−\mathrm{cos}\:{x}}{\mathrm{sin}\:{x}}=\frac{\mathrm{3}}{\mathrm{5}} \\…

A-certain-person-s-blood-preassure-is-modelled-by-the-function-p-t-115-25-sin-160pit-where-p-t-is-the-pressure-in-mmHg-at-time-t-measured-in-minutes-a-Find-the-number-of-heartbeats-per-minute-b

Question Number 132866 by bramlexs22 last updated on 17/Feb/21 $$\mathrm{A}\:\mathrm{certain}\:\mathrm{person}'\mathrm{s}\:\mathrm{blood}\:\mathrm{preassure} \\ $$$$\mathrm{is}\:\mathrm{modelled}\:\mathrm{by}\:\mathrm{the}\:\mathrm{function} \\ $$$$\mathrm{p}\left(\mathrm{t}\right)=\mathrm{115}+\mathrm{25}\:\mathrm{sin}\:\left(\mathrm{160}\pi\mathrm{t}\right) \\ $$$$\mathrm{where}\:\mathrm{p}\left(\mathrm{t}\right)\:\mathrm{is}\:\mathrm{the}\:\mathrm{pressure}\:\mathrm{in}\:\mathrm{mmHg} \\ $$$$\mathrm{at}\:\mathrm{time}\:\mathrm{t}\:\mathrm{measured}\:\mathrm{in}\:\mathrm{minutes}. \\ $$$$\left(\mathrm{a}\right)\:\mathrm{Find}\:\mathrm{the}\:\mathrm{number}\:\mathrm{of}\:\mathrm{heartbeats}\:\mathrm{per}\:\mathrm{minute} \\ $$$$\left(\mathrm{b}\right)\:\mathrm{Find}\:\mathrm{the}\:\mathrm{blood}\:\mathrm{preassure} \\ $$$$\mathrm{reading}.\:\mathrm{How}\:\mathrm{does}\:\mathrm{this}\:\mathrm{compare}\: \\…