Question Number 159322 by Ar Brandon last updated on 15/Nov/21 $$\mathrm{P}\left(\mathrm{z}\right)=\left(\mathrm{1}+{i}\sqrt{\mathrm{3}}\right){z}^{\mathrm{2}} −\left(−\mathrm{4}+\mathrm{4}{i}\right){z}+\mathrm{2}{i}\mathrm{cos}\left(\frac{\pi}{\mathrm{5}}\right)−\mathrm{2sin}\left(\frac{\pi}{\mathrm{5}}\right) \\ $$$$\mathrm{Let}\:{S}\:\mathrm{denote}\:\mathrm{the}\:\mathrm{sum}\:\mathrm{of}\:\mathrm{roots}\:\mathrm{of}\:\mathrm{P}\left({z}\right) \\ $$$$\left.\mathrm{a}\right)\:\mathrm{Express}\:{S}\:\mathrm{in}\:\mathrm{algebraic}\:\mathrm{form}\:\mathrm{then}\:\mathrm{in}\:\mathrm{exponential}\:\mathrm{form}. \\ $$$$\mathrm{b}.\:\mathrm{Deduce}\:\mathrm{the}\:\mathrm{exact}\:\mathrm{values}\:\mathrm{of}\:\mathrm{cos}\left(\frac{\mathrm{5}\pi}{\mathrm{12}}\right)\:\mathrm{and}\:\mathrm{sin}\left(\frac{\mathrm{5}\pi}{\mathrm{12}}\right). \\ $$ Answered by mindispower last updated…
Question Number 28164 by abdo imad last updated on 21/Jan/18 $${simplify}\: \\ $$$${A}={cos}^{\mathrm{4}} \theta\:+{cos}^{\mathrm{4}} \left(\theta+\frac{\pi}{\mathrm{4}}\right)\:+{cos}^{\mathrm{4}} \left(\theta\:+\frac{\mathrm{2}\pi}{\mathrm{4}}\right)\:+{cos}^{\mathrm{4}} \left(\theta\:+\frac{\mathrm{3}\pi}{\mathrm{4}}\right). \\ $$ Answered by ajfour last updated on…
Question Number 28163 by abdo imad last updated on 21/Jan/18 $${let}\:{give}\:{z}=\:{e}^{{i}\frac{\mathrm{2}\pi}{\mathrm{5}\:}} \:\:\:\:{and}\:\:{a}=\:{z}\:+{z}^{\mathrm{4}} \:\:\:\:,\:\:\:{b}=\:{z}^{\mathrm{2}} +{z}^{\mathrm{3}} \\ $$$${find}\:{a}\:{equation}\:{wich}\:{have}\:{a}\:{and}\:{for}\:{rootsthen}\:{find} \\ $$$${the}\:{values}\:{of}\:{cos}\left(\frac{\mathrm{2}\pi}{\left.\mathrm{5}\right)}\right),\:{sin}\left(\frac{\mathrm{2}\pi}{\mathrm{5}}\right),{cos}\left(\frac{\mathrm{4}\pi}{\mathrm{5}}\right)\:,{sin}\left(\frac{\mathrm{4}\pi}{\mathrm{5}}\right)\:,{cos}\left(\frac{\pi}{\mathrm{5}}\right). \\ $$ Terms of Service Privacy Policy…
Question Number 93689 by oustmuchiya@gmail.com last updated on 14/May/20 $${simply}:\frac{\left({cos}\mathrm{2}\Theta−\boldsymbol{{i}}{sin}\mathrm{2}\Theta\right)^{\mathrm{7}} \left({cos}\mathrm{3}\Theta+\boldsymbol{{i}}{sin}\mathrm{3}\Theta\right)^{−\mathrm{5}} }{\left({cos}\mathrm{4}\Theta+\boldsymbol{{i}}{sin}\mathrm{4}\Theta\right)^{\mathrm{12}} \left({cos}\mathrm{5}\Theta−\boldsymbol{{i}}{sin}\mathrm{5}\Theta\right)^{−\mathrm{6}} } \\ $$ Commented by PRITHWISH SEN 2 last updated on 14/May/20…
Question Number 159146 by tounghoungko last updated on 13/Nov/21 $${Find}\:{the}\:{absolute}\:{extrema}\:{of} \\ $$$${f}\left({x}\right)=\:\mathrm{2}\:\mathrm{csc}\:{x}\:+\:\mathrm{cot}\:{x}\:{on}\:{the}\: \\ $$$${interval}\:\left(\frac{\pi}{\mathrm{2}},\:\frac{\mathrm{3}\pi}{\mathrm{2}}\:\right] \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 159121 by physicstutes last updated on 13/Nov/21 $$\mathrm{Consider} \\ $$$${f}\left({x}\right)\:=\:{x}^{\mathrm{3}} \:+\:\mathrm{2}{x}\:−\mathrm{1}. \\ $$$$\mathrm{Use}\:\mathrm{the}\:\mathrm{intermidiate}\:\mathrm{value}\:\mathrm{theorem}\:\mathrm{and} \\ $$$$\mathrm{the}\:\mathrm{Rolle}\:\mathrm{theorem}\:\mathrm{to}\:\mathrm{establish}\:\mathrm{that}\:\mathrm{the} \\ $$$$\mathrm{equation}\:{f}\left({x}\right)\:=\:\mathrm{0}\:\mathrm{has}\:\mathrm{a}\:\mathrm{unique}\:\mathrm{solution} \\ $$$$\left.\mathrm{denoted}\:{a}_{\mathrm{0}} \in\right]\:\mathrm{0},\mathrm{1}\left[.\:\right. \\ $$ Terms…
Question Number 93571 by prince 5 last updated on 13/May/20 $${Prove}\:{that}\:\frac{\mathrm{1}−{tan}^{\mathrm{3}} \theta}{\mathrm{1}+{tan}^{\mathrm{3}} \theta}\:=\mathrm{1}−\mathrm{2}{sin}^{\mathrm{2}} \theta \\ $$ Commented by mr W last updated on 13/May/20 $${you}\:{can}'{t}\:{prove}\:{something}\:{which}\:{is}\:…
Question Number 159071 by physicstutes last updated on 12/Nov/21 $$\mathrm{Determine}\:\mathrm{the}\:\mathrm{cardinality}\:\mathrm{and}\:\mathrm{power} \\ $$$$\mathrm{set}\:\mathrm{of} \\ $$$${B}\:=\:\left\{\left\{{a},{b},{c}\right\},\left\{{d},{e}\right\},\left\{{f},{g},{h},{i}\right\}\right. \\ $$ Answered by Rasheed.Sindhi last updated on 12/Nov/21 $$\mathrm{cardinality}\:\mathrm{of}\:\mathrm{B}=\mathrm{3},\:\mathrm{because}\:\mathrm{B} \\…
Question Number 27958 by bmind4860 last updated on 17/Jan/18 $${For}\:\alpha\in{R},\:{cos}\alpha{cosx}+{siny}\geqslant{sinx},\:\forall{x}\in{R}, \\ $$$${then}\:{find}\:{the}\:{sum}\:{of}\:{the}\:{possible}\:{values} \\ $$$${of}\:{sin}\alpha+{siny}. \\ $$ Answered by ajfour last updated on 17/Jan/18 $$\:\:\:\:\mathrm{sin}\:{y}\:\geqslant\:\mathrm{sin}\:{x}−\mathrm{cos}\:\alpha\mathrm{cos}\:{x} \\…
Question Number 159030 by cortano last updated on 12/Nov/21 $$\:\left(\mathrm{arcsin}\:\left(\mathrm{cos}\:\mathrm{93}°\right)\right)^{\mathrm{2}} =? \\ $$ Answered by mr W last updated on 12/Nov/21 $$\mathrm{cos}\:\mathrm{93}°=−\mathrm{sin}\:\mathrm{3}°=−\mathrm{sin}\:\left(\frac{\pi}{\mathrm{60}}\right) \\ $$$${arcsin}\left(\mathrm{cos}\:\mathrm{93}°\right)={arcsin}\left(−\mathrm{sin}\:\frac{\pi}{\mathrm{60}}\right)=−\frac{\pi}{\mathrm{60}} \\…