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Category: Trigonometry

If-symbols-have-their-usual-meaning-then-1-r-2-1-r-1-2-1-r-2-2-1-r-3-2-1-a-2-b-2-c-2-s-2-2-a-2-b-2-c-2-3-a-2-b-2-c-2-2-4-a-b-

Question Number 23721 by Tinkutara last updated on 06/Nov/17 $$\mathrm{If}\:\mathrm{symbols}\:\mathrm{have}\:\mathrm{their}\:\mathrm{usual}\:\mathrm{meaning} \\ $$$$\mathrm{then}\:\frac{\mathrm{1}}{{r}^{\mathrm{2}} }\:+\:\frac{\mathrm{1}}{{r}_{\mathrm{1}} ^{\mathrm{2}} }\:+\:\frac{\mathrm{1}}{{r}_{\mathrm{2}} ^{\mathrm{2}} }\:+\:\frac{\mathrm{1}}{{r}_{\mathrm{3}} ^{\mathrm{2}} }\:= \\ $$$$\left(\mathrm{1}\right)\:\frac{{a}^{\mathrm{2}} \:+\:{b}^{\mathrm{2}} \:+\:{c}^{\mathrm{2}} }{{s}^{\mathrm{2}} }…

Question-154748

Question Number 154748 by imjagoll last updated on 21/Sep/21 Answered by ARUNG_Brandon_MBU last updated on 21/Sep/21 $$\mathrm{sin}\left(\mathrm{3log}_{\left(\mathrm{2sin}{x}\right)} \sqrt[{\mathrm{3}}]{\pi}\right)=\frac{\mathrm{1}}{\mathrm{2}}\:\Rightarrow\mathrm{log}_{\left(\mathrm{2sin}{x}\right)} \pi=\frac{\pi}{\mathrm{6}} \\ $$$$\Rightarrow\mathrm{log}_{\pi} \left(\mathrm{2sin}{x}\right)=\frac{\mathrm{6}}{\pi}\:\Rightarrow\mathrm{sin}{x}=\frac{\mathrm{1}}{\mathrm{2}}\pi^{\frac{\mathrm{6}}{\pi}} \\ $$$$\Rightarrow{x}=\mathrm{arcsin}\left(\frac{\mathrm{1}}{\mathrm{2}}\pi^{\frac{\mathrm{6}}{\pi}} \right)…

cos-x-sin-x-1-2-cos-x-sin-x-3-8-pi-lt-x-lt-2pi-cos-x-sin-x-

Question Number 89193 by jagoll last updated on 16/Apr/20 $$\mathrm{cos}\:{x}−\mathrm{sin}\:{x}\:=\frac{\mathrm{1}}{\mathrm{2}} \\ $$$$\mathrm{cos}\:{x}\:\mathrm{sin}\:{x}\:=\:\frac{\mathrm{3}}{\mathrm{8}}\:,\:\pi\:<\:{x}\:<\:\mathrm{2}\pi \\ $$$$\mathrm{cos}\:{x}\:+\:\mathrm{sin}\:{x}\:=? \\ $$ Commented by Tony Lin last updated on 16/Apr/20 $$\because\pi<{x}<\mathrm{2}\pi…

If-sin-3-sin-3-sin-sin-cos-and-cos-0-then-which-of-the-values-of-does-not-satisfy-the-given-equation-1-npi-1-n-pi-6-n-I-2-npi-1-n-pi-10-

Question Number 23648 by Tinkutara last updated on 03/Nov/17 $$\mathrm{If}\:\mathrm{sin}\left(\mathrm{3}\theta\:+\:\alpha\right)\:+\:\mathrm{sin}\left(\mathrm{3}\theta\:−\:\alpha\right)\:+\:\mathrm{sin}\left(\alpha\:−\:\theta\right) \\ $$$$−\:\mathrm{sin}\left(\alpha\:+\:\theta\right)\:=\:\mathrm{cos}\alpha\:\mathrm{and}\:\mathrm{cos}\alpha\:\neq\:\mathrm{0},\:\mathrm{then} \\ $$$$\mathrm{which}\:\mathrm{of}\:\mathrm{the}\:\mathrm{values}\:\mathrm{of}\:\theta\:\mathrm{does}\:\mathrm{not}\:\mathrm{satisfy} \\ $$$$\mathrm{the}\:\mathrm{given}\:\mathrm{equation}? \\ $$$$\left(\mathrm{1}\right)\:{n}\pi\:+\:\left(−\mathrm{1}\right)^{{n}} \:\frac{\pi}{\mathrm{6}},\:{n}\:\in\:{I} \\ $$$$\left(\mathrm{2}\right)\:{n}\pi\:+\:\left(−\mathrm{1}\right)^{{n}} \:\frac{\pi}{\mathrm{10}},\:{n}\:\in\:{I} \\ $$$$\left(\mathrm{3}\right)\:{n}\pi\:+\:\left(−\mathrm{1}\right)^{{n}} \:\frac{\pi}{\mathrm{5}},\:{n}\:\in\:{I}…