Menu Close

Category: Trigonometry

Given-sin-5x-38-cos-2x-16-0-x-90-find-the-value-of-x-

Question Number 161060 by pete last updated on 11/Dec/21 $$\mathrm{Given}\:\mathrm{sin}\left(\mathrm{5x}−\mathrm{38}\right)=\mathrm{cos}\left(\mathrm{2x}+\mathrm{16}\right),\:\mathrm{0}°\leqslant\mathrm{x}\leqslant\mathrm{90}°, \\ $$$$\mathrm{find}\:\mathrm{the}\:\mathrm{value}\:\mathrm{of}\:\mathrm{x} \\ $$ Commented by cortano last updated on 11/Dec/21 $$\:{recall}\:\mathrm{sin}\:\left(\mathrm{90}°−{x}\right)=\:\mathrm{cos}\:{x} \\ $$$$\Leftrightarrow\:\mathrm{sin}\:\left(\mathrm{5}{x}−\mathrm{38}°\right)=\:\mathrm{sin}\:\left(\mathrm{90}°−\left(\mathrm{128}°−\mathrm{5}{x}\right)\right)=\mathrm{cos}\:\left(\mathrm{128}°−\mathrm{5}{x}\right) \\…

1-sin10-3-cos10-

Question Number 95524 by Abdulrahman last updated on 25/May/20 $$\frac{\mathrm{1}}{\mathrm{sin10}}−\frac{\sqrt{\mathrm{3}}}{\mathrm{cos10}}=? \\ $$ Commented by PRITHWISH SEN 2 last updated on 25/May/20 $$\frac{\mathrm{cos}\:\mathrm{10}−\sqrt{\mathrm{3}}\mathrm{sin}\:\mathrm{10}}{\mathrm{sin}\:\mathrm{10cos}\:\mathrm{10}}\:=\:\mathrm{4}\frac{\left(\frac{\mathrm{1}}{\mathrm{2}}\mathrm{cos}\:\mathrm{10}−\frac{\sqrt{\mathrm{3}}}{\mathrm{2}}\mathrm{sin}\:\mathrm{10}\right)}{\mathrm{2sin}\:\mathrm{10cos}\:\mathrm{10}} \\ $$$$=\mathrm{4}.\frac{\mathrm{sin}\:\mathrm{30}.\mathrm{cos}\:\mathrm{10}−\mathrm{cos}\:\mathrm{30}.\mathrm{sin}\:\mathrm{10}}{\mathrm{sin}\:\mathrm{20}}\:=\mathrm{4}.\frac{\mathrm{sin}\:\left(\mathrm{30}−\mathrm{10}\right)}{\mathrm{sin}\:\mathrm{20}} \\…

3cos-2-x-3cos-x-sin-x-2sin-x-1-x-0-2pi-

Question Number 95495 by i jagooll last updated on 25/May/20 $$\mathrm{3cos}\:^{\mathrm{2}} {x}\:−\:\mathrm{3cos}\:{x}\:\mathrm{sin}\:{x}\:+\:\mathrm{2sin}\:{x}\:=\:\mathrm{1} \\ $$$${x}\:\in\:\left[\:\mathrm{0},\:\mathrm{2}\pi\:\right]\: \\ $$ Answered by bobhans last updated on 25/May/20 $$\mathrm{3}−\mathrm{3sin}\:^{\mathrm{2}} \mathrm{x}−\mathrm{3sin}\:\mathrm{xcos}\:\mathrm{x}\:+\mathrm{2sin}\:\mathrm{x}\:=\:\mathrm{1}…

0-pi-find-he-values-of-n-1-1-n-cos-n-and-n-1-1-n-sin-n-

Question Number 29847 by abdo imad last updated on 12/Feb/18 $$\left.\theta\:\in\right]\mathrm{0},\pi\left[\:\:\:{find}\:{he}\:{values}\:{of}\:\:\sum_{{n}=\mathrm{1}} ^{\infty} \:\frac{\mathrm{1}}{{n}}{cos}\left({n}\theta\right)\:{and}\right. \\ $$$$\sum_{{n}=\mathrm{1}} ^{\infty} \:\frac{\mathrm{1}}{{n}}{sin}\left({n}\theta\right)\:. \\ $$ Terms of Service Privacy Policy Contact:…

find-1-cos-4-pi-9-1-cos-4-3pi-9-1-cos-4-5pi-9-1-cos-4-7pi-9-

Question Number 29834 by abdo imad last updated on 12/Feb/18 $${find}\:\:\:\:\frac{\mathrm{1}}{{cos}^{\mathrm{4}} \left(\frac{\pi}{\mathrm{9}}\right)}\:+\frac{\mathrm{1}}{{cos}^{\mathrm{4}} \left(\frac{\mathrm{3}\pi}{\mathrm{9}}\right)}\:+\:\frac{\mathrm{1}}{{cos}^{\mathrm{4}} \left(\frac{\mathrm{5}\pi}{\mathrm{9}}\right)}\:+\frac{\mathrm{1}}{{cos}^{\mathrm{4}} \left(\frac{\mathrm{7}\pi}{\mathrm{9}}\right)}\:. \\ $$ Commented by MJS last updated on 14/Feb/18 $$=\mathrm{1120}\:\mathrm{but}\:\mathrm{it}\:\mathrm{takes}\:\mathrm{quite}\:\mathrm{some}…