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Category: Trigonometry

Question-93940

Question Number 93940 by seedhamaieng@gmail.com last updated on 16/May/20 Commented by Tony Lin last updated on 16/May/20 $${cos}^{−\mathrm{1}} \frac{\mathrm{4}}{\mathrm{5}}={tan}^{−\mathrm{1}} \frac{\mathrm{3}}{\mathrm{4}} \\ $$$${tan}^{−\mathrm{1}} \frac{\mathrm{3}}{\mathrm{4}}+{tan}^{−\mathrm{1}} \frac{\mathrm{2}}{\mathrm{5}} \\…

P-z-1-i-3-z-2-4-4i-z-2icos-pi-5-2sin-pi-5-Let-S-denote-the-sum-of-roots-of-P-z-a-Express-S-in-algebraic-form-then-in-exponential-form-b-Deduce-the-exact-values-of-cos-5pi-12-and-s

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…

let-give-z-e-i-2pi-5-and-a-z-z-4-b-z-2-z-3-find-a-equation-wich-have-a-and-for-rootsthen-find-the-values-of-cos-2pi-5-sin-2pi-5-cos-4pi-5-sin-4pi-5-cos-

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…

simply-cos2-isin2-7-cos3-isin3-5-cos4-isin4-12-cos5-isin5-6-

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…

Find-the-absolute-extrema-of-f-x-2-csc-x-cot-x-on-the-interval-pi-2-3pi-2-

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

Consider-f-x-x-3-2x-1-Use-the-intermidiate-value-theorem-and-the-Rolle-theorem-to-establish-that-the-equation-f-x-0-has-a-unique-solution-denoted-a-0-0-1-

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…

Determine-the-cardinality-and-power-set-of-B-a-b-c-d-e-f-g-h-i-

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} \\…