cos1-cos2-cos3-cos270-

Question Number 57127 by ANTARES VY last updated on 30/Mar/19

$$\left\{\boldsymbol{\mathrm{cos}}\mathrm{1}°\right\}+\left\{\boldsymbol{\mathrm{cos}}\mathrm{2}°\right\}+\left\{\boldsymbol{\mathrm{cos}}\mathrm{3}°\right\}+….+\left\{\boldsymbol{\mathrm{cos}}\mathrm{270}\right\}=? \\ $$

Commented by tanmay.chaudhury50@gmail.com last updated on 30/Mar/19

$$\boldsymbol{{source}}\:\boldsymbol{{S}}.\boldsymbol{{L}}\:\boldsymbol{{Loney}}\:\boldsymbol{{great}}\:\boldsymbol{{mathematician}} \\ $$

Commented by Tawa1 last updated on 30/Mar/19

$$\mathrm{from}\:\mathrm{the}\:\mathrm{general}\:\mathrm{formular}: \\ $$$$\mathrm{compare}\:\mathrm{with}…. \\ $$$$\:\:\:\mathrm{cos}\left(\alpha\right)\:+\:\mathrm{cos}\left(\mathrm{2}\alpha\right)\:+\:\mathrm{cos}\left(\mathrm{3}\alpha\right)\:+\:…\:+\:\mathrm{cos}\left(\mathrm{n}\alpha\right) \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:=\:\:\frac{\mathrm{cos}\left[\left(\frac{\mathrm{n}\:+\:\mathrm{1}}{\mathrm{2}}\right)\alpha\right]\:\mathrm{sin}\left(\frac{\mathrm{n}\alpha}{\mathrm{2}}\right)}{\mathrm{sin}\left(\frac{\alpha}{\mathrm{2}}\right)} \\ $$$$\alpha\:\:=\:\:\mathrm{1},\:\:\:\:\mathrm{n}\:=\:\mathrm{270} \\ $$$$\:\:\:\mathrm{cos}\left(\mathrm{1}\right)\:+\:\mathrm{cos}\left(\mathrm{2}\right)\:+\:\mathrm{cos}\left(\mathrm{3}\right)\:+\:…\:+\:\mathrm{cos}\left(\mathrm{270}\right) \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:=\:\:\frac{\mathrm{cos}\left[\left(\frac{\mathrm{270}\:+\:\mathrm{1}}{\mathrm{2}}\right)\right]\:\mathrm{sin}\left(\frac{\mathrm{270}}{\mathrm{2}}\right)}{\mathrm{sin}\left(\frac{\mathrm{1}}{\mathrm{2}}\right)} \\ $$$$\:\:\:\mathrm{cos}\left(\mathrm{1}\right)\:+\:\mathrm{cos}\left(\mathrm{2}\right)\:+\:\mathrm{cos}\left(\mathrm{3}\right)\:+\:…\:+\:\mathrm{cos}\left(\mathrm{270}\right) \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:=\:\:\frac{\mathrm{cos}\left[\left(\mathrm{135}.\mathrm{5}\right)\right]\:\mathrm{sin}\left(\mathrm{135}\right)}{\mathrm{sin}\left(\mathrm{0}.\mathrm{5}\right)} \\ $$$$\:\:\:\mathrm{cos}\left(\mathrm{1}\right)\:+\:\mathrm{cos}\left(\mathrm{2}\right)\:+\:\mathrm{cos}\left(\mathrm{3}\right)\:+\:…\:+\:\mathrm{cos}\left(\mathrm{270}\right)\:\:\:=\:\:−\:\mathrm{57}.\mathrm{7943} \\ $$

Commented by ANTARES VY last updated on 30/Mar/19

$$? \\ $$

Commented by tanmay.chaudhury50@gmail.com last updated on 30/Mar/19

$${convert}\:{degree}\left[{to}\:{radian}\:\:\rightarrow\mathrm{1}^{{o}} =\frac{\pi}{\mathrm{180}}{radian}…\right. \\ $$

Commented by tanmay.chaudhury50@gmail.com last updated on 30/Mar/19

Commented by tanmay.chaudhury50@gmail.com last updated on 30/Mar/19

Commented by tanmay.chaudhury50@gmail.com last updated on 30/Mar/19

Commented by tanmay.chaudhury50@gmail.com last updated on 30/Mar/19

Commented by tanmay.chaudhury50@gmail.com last updated on 30/Mar/19

Commented by tanmay.chaudhury50@gmail.com last updated on 30/Mar/19

Commented by peter frank last updated on 30/Mar/19

$${thank}\:{you}\:{for}\:{sharing} \\ $$

Commented by malwaan last updated on 31/Mar/19

$$\boldsymbol{{can}}\:\boldsymbol{{you}}\:\boldsymbol{{send}}\:\boldsymbol{{link}}\:\boldsymbol{{to}} \\ $$$$\boldsymbol{{dowload}}\:\boldsymbol{{the}}\:\boldsymbol{{book}}\:? \\ $$$$\boldsymbol{{please}} \\ $$

Commented by ANTARES VY last updated on 31/Mar/19

$$\boldsymbol{\mathrm{yes}} \\ $$

Commented by ANTARES VY last updated on 31/Mar/19

$$\boldsymbol{\mathrm{do}}\:\boldsymbol{\mathrm{you}}\:\boldsymbol{\mathrm{have}}\:\:\boldsymbol{\mathrm{a}}\:\:\boldsymbol{\mathrm{math}} \\ $$$$\boldsymbol{\mathrm{group}}\:\boldsymbol{\mathrm{or}}\:\:\boldsymbol{\mathrm{telegramm}}? \\ $$

Commented by tanmay.chaudhury50@gmail.com last updated on 31/Mar/19

Commented by tanmay.chaudhury50@gmail.com last updated on 31/Mar/19

Commented by tanmay.chaudhury50@gmail.com last updated on 01/Apr/19

Commented by Tawa1 last updated on 01/Apr/19

$$\mathrm{Sir},\:\mathrm{please}\:\mathrm{give}\:\mathrm{me}\:\mathrm{hint}\:\mathrm{on}\:\mathrm{how}\:\mathrm{to}\:\mathrm{download}\:\mathrm{good}\:\mathrm{textbook} \\ $$$$\mathrm{on}\:\mathrm{archive}.\mathrm{org} \\ $$

Commented by tanmay.chaudhury50@gmail.com last updated on 01/Apr/19

$${click}\:{on}\:{book}\:{then}\:{scroll}\:{down}\:\:{apply}\:{down}\:{load}\:{option} \\ $$

Commented by tanmay.chaudhury50@gmail.com last updated on 01/Apr/19

Commented by Tawa1 last updated on 01/Apr/19

$$\mathrm{What}\:\mathrm{will}\:\mathrm{i}\:\mathrm{search}\:\mathrm{for}\:\mathrm{or}\:\mathrm{how}\:\mathrm{can}\:\mathrm{i}\:\mathrm{search}\:\mathrm{for}\:\mathrm{a}\:\mathrm{particular}\: \\ $$$$\mathrm{textbook}\:\mathrm{sir}.\:\:\mathrm{Sorry}\:\mathrm{for}\:\mathrm{disturbing}\:\mathrm{sir}. \\ $$

Commented by ANTARES VY last updated on 01/Apr/19

$$\boldsymbol{\mathrm{adress}} \\ $$

Commented by tanmay.chaudhury50@gmail.com last updated on 01/Apr/19

$${you}\:{sesrch}\:{topic}\:{wise}\:{such}\:{as}\:{algebra}\:{or}\:{Trigonometry} \\ $$$${orcalculus}\:{or}\:{graph}\:{or}\:{coordinate}\:{geometry} \\ $$$${or}\:{physics}..{mechanics}\:\:{or}\:{heat}\:\:{or}\:{electricity} \\ $$

Commented by Tawa1 last updated on 01/Apr/19

$$\mathrm{God}\:\mathrm{bless}\:\mathrm{you}\:\mathrm{sir} \\ $$

Terms of Service
Privacy Policy
Contact: info@tinkutara.com