Question Number 187311 by anurup last updated on 16/Feb/23 $$\mathrm{If}\:{f}_{{k}} \left({x}\right)=\frac{\mathrm{1}}{{k}}\left(\mathrm{sin}\:^{{k}} {x}+\mathrm{cos}\:^{{k}} {x}\right)\:\mathrm{find}\:{f}_{\mathrm{4}} \left({x}\right)−{f}_{\mathrm{6}} \left({x}\right) \\ $$$${f}_{\mathrm{4}} \left({x}\right)−{f}_{\mathrm{6}} \left({x}\right)=\frac{\mathrm{1}}{\mathrm{4}}\left(\mathrm{sin}\:^{\mathrm{4}} {x}\:+\mathrm{cos}\:^{\mathrm{4}} {x}\right)−\frac{\mathrm{1}}{\mathrm{6}}\left(\mathrm{sin}\:^{\mathrm{6}} {x}+\mathrm{cos}\:^{\mathrm{6}} {x}\right) \\ $$$$\:\:\:=\frac{\mathrm{1}}{\mathrm{2}}\mathrm{sin}\:^{\mathrm{4}}…
Question Number 121705 by bemath last updated on 11/Nov/20 Answered by MJS_new last updated on 11/Nov/20 $$\mathrm{cis}\:{x}\:=\mathrm{cos}\:{x}\:+\mathrm{i}\:\mathrm{sin}\:{x}\:=\mathrm{e}^{\mathrm{i}{x}} \\ $$$$\mathrm{16}°=\frac{\mathrm{4}\pi}{\mathrm{45}};\:\mathrm{44}°=\frac{\mathrm{11}\pi}{\mathrm{45}};\:\mathrm{62}°=\frac{\mathrm{31}\pi}{\mathrm{90}} \\ $$$$\frac{\mathrm{12e}^{\frac{\mathrm{4}\pi}{\mathrm{45}}\mathrm{i}} }{\mathrm{3e}^{\frac{\mathrm{11}\pi}{\mathrm{45}}\mathrm{i}} \mathrm{2e}^{\frac{\mathrm{31}\pi}{\mathrm{90}}\mathrm{i}} }=\mathrm{2e}^{\mathrm{i}\pi\left(\frac{\mathrm{4}}{\mathrm{45}}−\frac{\mathrm{11}}{\mathrm{45}}−\frac{\mathrm{31}}{\mathrm{90}}\right)} =\mathrm{2e}^{−\mathrm{i}\frac{\pi}{\mathrm{2}}}…
Question Number 121689 by bemath last updated on 11/Nov/20 $$\:{Let}\:{a}\:{and}\:{b}\:{be}\:{real}\:{numbers}\:{such} \\ $$$${that}\:\begin{cases}{\mathrm{sin}\:{a}\:+\:\mathrm{sin}\:{b}\:=\:\frac{\sqrt{\mathrm{2}}}{\mathrm{2}}}\\{\mathrm{cos}\:{a}\:+\:\mathrm{cos}\:{b}\:=\:\frac{\sqrt{\mathrm{6}}}{\mathrm{2}}}\end{cases} \\ $$$${Evaluate}\:\mathrm{sin}\:\left({a}+{b}\right).\: \\ $$ Answered by liberty last updated on 11/Nov/20 $$\mathrm{squaring}\:\mathrm{the}\:\mathrm{both}\:\mathrm{equation}\:\mathrm{gives} \\…
Question Number 187144 by a.lgnaoui last updated on 14/Feb/23 $${determiner}\:{les}\:{elements} \\ $$$${demandes}\:\left({fig}\:{ci}−{joint}\right) \\ $$ Commented by a.lgnaoui last updated on 14/Feb/23 Terms of Service Privacy…
Question Number 121598 by TITA last updated on 09/Nov/20 $${find}\:{the}\:{solution}\:{of}\:{f}\left({x},{y},{z}\right)=\left(\mathrm{sin}\:{x}\right)\left(\mathrm{cos}\:{y}\right)\left(\mathrm{tan}\:{z}\right) \\ $$$${for}\:\mathrm{0}\leqslant{x},{y},{z}\leqslant\frac{\Pi}{\mathrm{4}}\: \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 121522 by benjo_mathlover last updated on 09/Nov/20 $$\mathrm{19}\:\mathrm{sin}\:\mathrm{2x}\:=\mathrm{37}\:\mathrm{cos}\:\mathrm{2x}\:+\mathrm{38}\:\mathrm{sin}\:^{\mathrm{2}} \mathrm{x}\: \\ $$$$\mathrm{find}\:\mathrm{the}\:\mathrm{value}\:\mathrm{of}\:\mathrm{tan}\:\mathrm{x}\:. \\ $$ Commented by liberty last updated on 09/Nov/20 $$\:\frac{\mathrm{38sin}\:\mathrm{xcos}\:\mathrm{x}}{\mathrm{cos}\:^{\mathrm{2}} \mathrm{x}}\:=\:\frac{\mathrm{37}\left(\mathrm{1}−\mathrm{2sin}\:^{\mathrm{2}} \mathrm{x}\right)}{\mathrm{cos}\:^{\mathrm{2}}…
Question Number 186996 by Mingma last updated on 12/Feb/23 Answered by aba last updated on 12/Feb/23 $$\mathrm{0}<\mathrm{ln}\left(\mathrm{3}/\mathrm{2}\right)<\mathrm{6}/\mathrm{13} \\ $$ Commented by MJS_new last updated on…
Question Number 186926 by cortano12 last updated on 12/Feb/23 Commented by cortano12 last updated on 12/Feb/23 Q2 A 6ft tall man is moving at a speed of 2ft/s towards a building with a window whose base is 10ft above the ground and the height of the window is 4ft. If the angle between the lines of the man’s gaze is up and down the window, find the rate of change of the angle when the man is 16ft away from the base of the building Answered by manxsol last updated on 12/Feb/23 $$\frac{{dx}}{{dt}}=−\mathrm{2}\frac{{ft}}{{s}}\:\:\:\:\:\:\:…
Question Number 121303 by talminator2856791 last updated on 06/Nov/20 $$\: \\ $$$$\: \\ $$$$\: \\ $$$$\: \\ $$$$\:\:\:\:\:\:\mathrm{cos}\:{x}\:−\:\sqrt{\mathrm{3}}\:\mathrm{sin}\:{x}\:=\:\mathrm{2}\:\mathrm{cos}\:\mathrm{2}{x} \\ $$$$\: \\ $$$$\: \\ $$ Commented…
Question Number 186830 by ajfour last updated on 11/Feb/23 Commented by ajfour last updated on 11/Feb/23 $${Find}\:{x}. \\ $$ Answered by ajfour last updated on…