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Category: Trigonometry

Question-87505

Question Number 87505 by Ar Brandon last updated on 04/Apr/20 Commented by MJS last updated on 04/Apr/20 $$\mathrm{the}\:\mathrm{same}\:\mathrm{old}\:\mathrm{question}\:\mathrm{the}\:\mathrm{1}.\mathrm{000}.\mathrm{000}.\mathrm{000th} \\ $$$$\mathrm{time}. \\ $$$$\mathrm{the}\:\mathrm{cable}\:\mathrm{hangs}\:\mathrm{down}\:\mathrm{40}\:\mathrm{meters}\:\mathrm{from}\:\mathrm{each} \\ $$$$\mathrm{pole}.\:\mathrm{if}\:\mathrm{the}\:\mathrm{cable}\:\mathrm{is}\:\mathrm{80}\:\mathrm{meters}\:\mathrm{long},\:\mathrm{there}'\mathrm{s} \\…

sin-4-x-sin-4-x-pi-4-1-4-x-0-2pi-

Question Number 87488 by jagoll last updated on 04/Apr/20 $$\mathrm{sin}\:^{\mathrm{4}} \mathrm{x}\:+\:\mathrm{sin}\:^{\mathrm{4}} \left(\mathrm{x}+\frac{\pi}{\mathrm{4}}\right)\:=\:\frac{\mathrm{1}}{\mathrm{4}} \\ $$$$\mathrm{x}\:\in\:\left[\:\mathrm{0},\mathrm{2}\pi\:\right]\: \\ $$ Commented by john santu last updated on 05/Apr/20 $$\left(\mathrm{2sin}^{\mathrm{2}}…

If-a-b-and-A-of-a-triangle-are-fixed-and-two-possible-values-of-the-third-side-be-c-1-and-c-2-such-that-c-1-2-c-1-c-2-c-2-2-a-2-then-find-angle-A-

Question Number 21889 by ajfour last updated on 06/Oct/17 $${If}\:{a},{b},\:{and}\:{A}\:{of}\:{a}\:{triangle}\:\:{are}\: \\ $$$${fixed}\:{and}\:{two}\:{possible}\:{values}\:{of}\:{the}\: \\ $$$${third}\:{side}\:{be}\:{c}_{\mathrm{1}} {and}\:{c}_{\mathrm{2}} {such}\:{that} \\ $$$$\boldsymbol{{c}}_{\mathrm{1}} ^{\mathrm{2}} +\boldsymbol{{c}}_{\mathrm{1}} \boldsymbol{{c}}_{\mathrm{2}} +\boldsymbol{{c}}_{\mathrm{2}} ^{\mathrm{2}} =\boldsymbol{{a}}^{\mathrm{2}} ,\:{then}\:{find}\:{angle}\:{A}.…

prove-that-sin-x-2-sin-x-sin-3x-sin-x-2sin-x-sin-3x-tan-2-x-2-

Question Number 87424 by Rio Michael last updated on 04/Apr/20 $$\mathrm{prove}\:\mathrm{that}\:\:\:\frac{\mathrm{sin}\:{x}\:−\:\mathrm{2}\:\mathrm{sin}\:{x}\:+\:\mathrm{sin}\:\mathrm{3}{x}}{\mathrm{sin}\:{x}\:+\:\mathrm{2sin}\:{x}\:+\:\mathrm{sin}\:\mathrm{3}{x}}\:\equiv\:−\mathrm{tan}^{\mathrm{2}} \left(\frac{{x}}{\mathrm{2}}\right) \\ $$ Commented by john santu last updated on 04/Apr/20 $$\frac{\mathrm{sin}\:\mathrm{3x}−\mathrm{sin}\:\mathrm{x}}{\mathrm{sin}\:\mathrm{3x}+\mathrm{3sin}\:\mathrm{x}}\:=\:\frac{\mathrm{2cos}\:\mathrm{2x}\:\mathrm{sin}\:\mathrm{x}}{\mathrm{3sin}\:\mathrm{x}−\mathrm{4sin}\:^{\mathrm{3}} \mathrm{x}+\mathrm{3sin}\:\mathrm{x}} \\…

if-equation-sin-x-sec-x-2tan-x-1-0-has-roots-x-1-amp-x-2-then-the-possible-value-of-sin-x-1-cos-x-2-a-4-5-b-3-4-c-4-3-d-3-2-e-2-

Question Number 87419 by john santu last updated on 04/Apr/20 $$\mathrm{if}\:\mathrm{equation}\:\mathrm{sin}\:\mathrm{x}\:+\:\mathrm{sec}\:\mathrm{x}\:−\mathrm{2tan}\:\mathrm{x}\:−\mathrm{1}\:=\:\mathrm{0} \\ $$$$\mathrm{has}\:\mathrm{roots}\:\mathrm{x}_{\mathrm{1}} \:\&\:\mathrm{x}_{\mathrm{2}} \:,\:\mathrm{then}\:\mathrm{the}\: \\ $$$$\mathrm{possible}\:\mathrm{value}\:\mathrm{of}\:\mathrm{sin}\:\mathrm{x}_{\mathrm{1}} −\mathrm{cos}\:\mathrm{x}_{\mathrm{2}} \:? \\ $$$$\left(\mathrm{a}\right)\:\mathrm{4}/\mathrm{5}\:\:\:\:\:\left(\mathrm{b}\right)\:\mathrm{3}/\mathrm{4}\:\:\:\:\:\left(\mathrm{c}\right)\:\mathrm{4}/\mathrm{3}\: \\ $$$$\left(\mathrm{d}\right)\:\mathrm{3}/\mathrm{2}\:\:\:\:\left(\mathrm{e}\right)\:\mathrm{2} \\ $$…

By-eliminating-show-that-x-2-y-2-if-x-sin-3-y-cos-3-sin-and-x-sin-y-cos-0-

Question Number 152715 by Tawa11 last updated on 31/Aug/21 $$\mathrm{By}\:\mathrm{eliminating}\:\:\theta,\:\:\:\mathrm{show}\:\mathrm{that}\:\:\:\:\:\mathrm{x}^{\mathrm{2}} \:\:\:=\:\:\:−\:\:\:\mathrm{y}^{\mathrm{2}} ,\:\:\:\:\:\: \\ $$$$\mathrm{if}\:\:\:\:\:\mathrm{x}\:\mathrm{sin}^{\mathrm{3}} \theta\:\:\:+\:\:\:\mathrm{y}\:\mathrm{cos}^{\mathrm{3}} \theta\:\:\:\:=\:\:\:\:\mathrm{sin}\theta\:\:\:\:\:\:\:\:\:\:\:\:\mathrm{and}\:\:\:\:\:\:\:\:\mathrm{x}\:\mathrm{sin}\theta\:\:\:\:−\:\:\:\mathrm{y}\:\mathrm{cos}\theta\:\:\:\:=\:\:\:\:\mathrm{0} \\ $$ Commented by Tawa11 last updated on 02/Sep/21…

If-1-n-sin-2-1-n-cos-2-1-n-find-tan-2-

Question Number 21453 by Joel577 last updated on 24/Sep/17 $$\mathrm{If}\: \\ $$$$\left(\mathrm{1}\:+\:{n}\right)\mathrm{sin}\:\mathrm{2}\theta\:+\:\left(\mathrm{1}\:−\:{n}\right)\mathrm{cos}\:\mathrm{2}\theta\:=\:\mathrm{1}\:+\:{n} \\ $$$$\mathrm{find}\:\mathrm{tan}\:\mathrm{2}\theta \\ $$ Answered by $@ty@m last updated on 24/Sep/17 $$\left(\mathrm{1}−{n}\right)\mathrm{cos}\:\mathrm{2}\theta=\left(\mathrm{1}+{n}\right)\left(\mathrm{1}−\mathrm{sin}\:\mathrm{2}\theta\right) \\…