Menu Close

Category: Trigonometry

Demonstrate-that-x-0-pi-2-tanx-1-cos-2x-sin-2x-

Question Number 75617 by mathocean1 last updated on 13/Dec/19 $$\left.\mathrm{Demonstrate}\:\mathrm{that}\:\forall\:\mathrm{x}\:\in\right]\mathrm{0};\frac{\pi}{\mathrm{2}}\left[\right. \\ $$$$\mathrm{tanx}=\frac{\mathrm{1}−\mathrm{cos}\left(\mathrm{2x}\right)}{\mathrm{sin}\left(\mathrm{2x}\right)} \\ $$ Commented by mind is power last updated on 13/Dec/19 $$\mathrm{use}\:\mathrm{cos}\left(\mathrm{2x}\right)=\mathrm{1}−\mathrm{2sin}^{\mathrm{2}} \left(\mathrm{x}\right)…

sin-2-x-sinx-4-3-x-0-pi-equation-sum-of-roots-in-range-

Question Number 141110 by Fikret last updated on 15/May/21 $${sin}^{\mathrm{2}} {x}+{sinx}=\frac{\mathrm{4}}{\mathrm{3}}\:\:\:\:\:\:\:,\:\:\:{x}\in\left[\mathrm{0},\pi\right] \\ $$$${equation}\:\:{sum}\:\:{of}\:{roots}\:{in}\:{range}? \\ $$ Answered by MJS_new last updated on 15/May/21 $${s}^{\mathrm{2}} +{s}−\frac{\mathrm{4}}{\mathrm{3}}=\mathrm{0}\wedge−\mathrm{1}\leqslant{s}\leqslant\mathrm{1}\:\Rightarrow\:{s}=−\frac{\mathrm{1}}{\mathrm{2}}+\frac{\sqrt{\mathrm{57}}}{\mathrm{6}} \\…

please-sirs-i-would-like-that-you-help-me-to-show-this-sin-pi-3-x-sin-pi-3-x-3-4-sin-2-x-

Question Number 75504 by mathocean1 last updated on 12/Dec/19 $$\mathrm{please}\:\mathrm{sirs}\:\mathrm{i}\:\mathrm{would}\:\mathrm{like}\:\mathrm{that}\:\mathrm{you}\:\mathrm{help}\:\mathrm{me}\:\mathrm{to} \\ $$$$\mathrm{show}\:\mathrm{this}: \\ $$$$\mathrm{sin}\left(\frac{\pi}{\mathrm{3}}+\mathrm{x}\right)\mathrm{sin}\left(\frac{\pi}{\mathrm{3}\:}−\mathrm{x}\right)=\frac{\mathrm{3}}{\mathrm{4}}−\mathrm{sin}^{\mathrm{2}} \mathrm{x} \\ $$ Answered by som(math1967) last updated on 12/Dec/19 $${sin}\left(\frac{\pi}{\mathrm{3}}\:+{x}\right){sin}\left(\frac{\pi}{\mathrm{3}}−{x}\right)…

Solve-it-in-pi-pi-sin-2x-cos-x-

Question Number 75502 by mathocean1 last updated on 12/Dec/19 $$\left.\mathrm{S}\left.\mathrm{olve}\:\mathrm{it}\:\mathrm{in}\:\right]−\pi;\pi\right] \\ $$$$\mathrm{sin}\left(\mathrm{2x}\right)=\mathrm{cos}\left(\mathrm{x}\right) \\ $$ Commented by mathmax by abdo last updated on 12/Dec/19 $${sin}\left(\mathrm{2}{x}\right)={cosx}\:\Leftrightarrow\:{sin}\left(\mathrm{2}{x}\right)={sin}\left(\frac{\pi}{\mathrm{2}}−{x}\right)\:\Leftrightarrow\mathrm{2}{x}=\frac{\pi}{\mathrm{2}}−{x}+\mathrm{2}{k}\pi\:{or} \\…

Question-9921

Question Number 9921 by Tawakalitu ayo mi last updated on 15/Jan/17 Answered by mrW1 last updated on 16/Jan/17 $$\mathrm{2}{x}=\mathrm{180}−\mathrm{50}−\mathrm{70}=\mathrm{60} \\ $$$$\Rightarrow{x}=\mathrm{30} \\ $$$${y}=\mathrm{180}−\mathrm{50}−{x}=\mathrm{100} \\ $$$${z}=\mathrm{180}−{x}−\left(\mathrm{70}+\mathrm{50}\right)=\mathrm{180}−\mathrm{30}−\mathrm{120}=\mathrm{30}…

Question-9920

Question Number 9920 by Tawakalitu ayo mi last updated on 15/Jan/17 Answered by mrW1 last updated on 16/Jan/17 $${x}=\mathrm{360}−\left(\mathrm{360}−\mathrm{290}\right)−\left(\mathrm{360}−\mathrm{320}\right) \\ $$$$=\mathrm{360}−\mathrm{70}−\mathrm{40} \\ $$$$=\mathrm{250} \\ $$$${or}…