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Category: Trigonometry

Question-124927

Question Number 124927 by bemath last updated on 07/Dec/20 Answered by liberty last updated on 07/Dec/20 $$\left(\mathrm{1}\right)\:\mathrm{sin}\:\mathrm{38}°\:=\:\frac{{x}+{y}}{\mathrm{8}}\:;\:{x}+{y}\:=\:\mathrm{8}.\mathrm{sin}\:\mathrm{38}° \\ $$$$\Rightarrow{x}+{y}\:=\:\mathrm{4}.\mathrm{9}\:{ft}\: \\ $$$$\left(\mathrm{2}\right)\:\mathrm{sin}\:\mathrm{52}°\:=\:\frac{{t}}{\mathrm{8}}\:;\:{t}\:=\:\mathrm{8}.\mathrm{sin}\:\mathrm{52}°\:=\:\mathrm{6}.\mathrm{3}\:{ft} \\ $$$$\left(\mathrm{3}\right)\:\mathrm{tan}\:\mathrm{20}°\:=\:\frac{{x}}{{t}}\:;\:{x}\:=\:{t}.\mathrm{tan}\:\mathrm{20}°\:=\:\mathrm{2}.\mathrm{3} \\ $$$${then}\:{we}\:{get}\:{y}\:=\:\mathrm{4}.\mathrm{9}−\mathrm{2}.\mathrm{3}\:=\:\mathrm{2}.\mathrm{6}\:{ft}…

sin-cos-1-3-2-

Question Number 59326 by prattushdas7@gmail.com last updated on 08/May/19 $${sin}\:{cos}^{−\mathrm{1}} \left(−\sqrt{\left.\mathrm{3}/\mathrm{2}\right)}\right. \\ $$ Commented by MJS last updated on 08/May/19 $$\mathrm{sin}\:\mathrm{cos}^{−\mathrm{1}} \:{x}\:=\mathrm{cos}\:\mathrm{sin}^{−\mathrm{1}} \:{x}\:=\sqrt{\mathrm{1}−{x}^{\mathrm{2}} } \\…

Witthout-using-mathematical-tables-or-calculator-find-in-surdform-radicals-the-value-tan22-5-

Question Number 59305 by pete last updated on 07/May/19 $$\mathrm{Witthout}\:\mathrm{using}\:\mathrm{mathematical}\:\mathrm{tables}\:\mathrm{or} \\ $$$$\mathrm{calculator},\:\mathrm{find},\mathrm{in}\:\mathrm{surdform}\left(\mathrm{radicals}\right) \\ $$$$,\:\mathrm{the}\:\mathrm{value}\:\mathrm{tan22}.\mathrm{5}° \\ $$ Answered by ajfour last updated on 07/May/19 $$\mathrm{tan}\:\mathrm{2}\theta=\frac{\mathrm{2tan}\:\theta}{\mathrm{1}−\mathrm{tan}\:^{\mathrm{2}} \theta}…

Question-59246

Question Number 59246 by hovea cw last updated on 06/May/19 Commented by MJS last updated on 06/May/19 $$\left(\mathrm{1}\right)\:\mathrm{doesn}'\mathrm{t}\:\mathrm{seem}\:\mathrm{to}\:\mathrm{have}\:\mathrm{a}\:“\mathrm{nice}''\:\mathrm{solution} \\ $$$$\mathrm{I}\:\mathrm{get}\:\sqrt{\mathrm{3}}\mathrm{tan}\:\mathrm{10}°\:\mathrm{cos}\:\mathrm{40}°\:\approx.\mathrm{233956} \\ $$ Commented by maxmathsup…

Question-190306

Question Number 190306 by cortano12 last updated on 31/Mar/23 Answered by Frix last updated on 31/Mar/23 $$\mathrm{Area}\:\mathrm{of}\:\mathrm{triangle}\:{u},\:{v},\:{w}\:\mathrm{is} \\ $$$$\frac{\sqrt{\left({u}+{v}+{w}\right)\left({u}+{v}−{w}\right)\left({u}+{w}−{v}\right)\left({v}+{w}−{u}\right)}}{\mathrm{4}}= \\ $$$$=\frac{\sqrt{\mathrm{2}\left({u}^{\mathrm{2}} {v}^{\mathrm{2}} +{u}^{\mathrm{2}} {w}^{\mathrm{2}} +{v}^{\mathrm{2}}…

In-AB-C-If-sin-A-1-2-2-3-A-

Question Number 190185 by mnjuly1970 last updated on 29/Mar/23 $$ \\ $$$$\:\:\:\:\:\:\mathrm{In}\:\mathrm{A}\overset{\Delta} {\mathrm{B}C}\:\::\:\: \\ $$$$ \\ $$$$\:\:\:\:\:\:\:\:\:\mathrm{If}\:,\:\mathrm{sin}\:\left(\hat {\mathrm{A}}\:\right)\:=\:\frac{\mathrm{1}}{\mathrm{2}\:\sqrt{\:\mathrm{2}+\:\sqrt{\mathrm{3}}}}\:\:\:\:\:\Rightarrow\:\:\:\:\:\hat {\mathrm{A}}\:=\:?\:\:\:\:\:\:\:\:\:\: \\ $$$$\:\:\:\:\:\:\:\:\: \\ $$ Commented by…

probar-con-h-0-sin-x-h-sin-x-h-sin-h-2-h-2-cos-x-h-2-

Question Number 59006 by arcana last updated on 03/May/19 $${probar}\:{con}\:{h}\neq\mathrm{0} \\ $$$$\frac{{sin}\left({x}+{h}\right)−{sin}\left({x}\right)}{{h}}=\frac{{sin}\left({h}/\mathrm{2}\right)}{{h}/\mathrm{2}}{cos}\left({x}+\frac{{h}}{\mathrm{2}}\right) \\ $$$$ \\ $$ Commented by arcana last updated on 25/May/19 $${usando}\:\:\mathrm{2}{sin}\left({x}\right){cos}\left({y}\right)={sin}\left({x}+{y}\right)−{sin}\left({y}−{x}\right) \\…