Category: Trigonometry

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…

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}…

Question Number 89047 by jagoll last updated on 15/Apr/20 $$\mathrm{cos}\:{x}+\mathrm{sin}\:{x}=\frac{\mathrm{4}}{\mathrm{5}} \\ $$$$\mathrm{5sin}\:{x}\:=\:? \\ $$ Commented by john santu last updated on 15/Apr/20 $$\pm\:\sqrt{\mathrm{1}−\mathrm{sin}\:^{\mathrm{2}} {x}}\:=\:\frac{\mathrm{4}}{\mathrm{5}}−\mathrm{sin}\:{x} \\…

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Question Number 23343 by ajfour last updated on 29/Oct/17 Commented by ajfour last updated on 29/Oct/17 $${Q}.\mathrm{23330}\:\left({solution}\right) \\ $$ Commented by Tinkutara last updated on…