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wu :: forums    riddles    medium (Moderators: william wu, SMQ, Icarus, ThudnBlunder, Eigenray, Grimbal, towr)    Trig Equation « Previous topic | Next topic » Pages: 1  Reply Notify of replies Send Topic Print    Author  Topic: Trig Equation  (Read 712 times) ThudnBlunder wu::riddles Moderator Uberpuzzler The dewdrop slides into the shining Sea     Gender: Posts: 4489 Trig Equation   « on: Oct 21st, 2008, 2:30pm » Quote Modify Find a necessary and sufficient condition on n so that the equation 2sin+ ncos = 7 IP Logged THE MEEK SHALL INHERIT THE EARTH.....................................................................er, if that's all right with the rest of you. Grimbal wu::riddles Moderator Uberpuzzler     Gender: Posts: 7527 Re: Trig Equation   « Reply #1 on: Oct 21st, 2008, 3:20pm » Quote Modify ... has a solution for some ?   IP Logged Michael Dagg Senior Riddler     Gender: Posts: 500 Re: Trig Equation   « Reply #2 on: Oct 21st, 2008, 4:12pm » Quote Modify As Grimbal noted, the result can't hold for all   alpha .  I smell a good algebraic discussion, let me guess: roots of unity... « Last Edit: Oct 21st, 2008, 4:14pm by Michael Dagg » IP Logged Regards, Michael Dagg Michael Dagg Senior Riddler     Gender: Posts: 500 Re: Trig Equation   « Reply #3 on: Oct 21st, 2008, 4:26pm » Quote Modify That is, if n is an integer.  Otherwise it is trivial. IP Logged Regards, Michael Dagg ThudnBlunder wu::riddles Moderator Uberpuzzler The dewdrop slides into the shining Sea     Gender: Posts: 4489 Re: Trig Equation   « Reply #4 on: Oct 21st, 2008, 5:50pm » Quote Modify on Oct 21st, 2008, 4:26pm, Michael Dagg wrote: That is, if n is an integer.  Otherwise it is trivial. n and yes, is restricted somewhat. IP Logged THE MEEK SHALL INHERIT THE EARTH.....................................................................er, if that's all right with the rest of you. teekyman Full Member     Gender: Posts: 199 Re: Trig Equation   « Reply #5 on: Oct 21st, 2008, 11:48pm » Quote Modify n needs to be at least 3? « Last Edit: Oct 22nd, 2008, 11:31am by teekyman » IP Logged ThudnBlunder wu::riddles Moderator Uberpuzzler The dewdrop slides into the shining Sea     Gender: Posts: 4489 Re: Trig Equation   « Reply #6 on: Oct 22nd, 2008, 12:36pm » Quote Modify on Oct 21st, 2008, 11:48pm, 1337b4k4 wrote: n needs to be at least 3? Yes. was that a guess? IP Logged THE MEEK SHALL INHERIT THE EARTH.....................................................................er, if that's all right with the rest of you. teekyman Full Member     Gender: Posts: 199 Re: Trig Equation   « Reply #7 on: Oct 22nd, 2008, 12:45pm » Quote Modify nope. a*sin() + b*cos() = (a+ b) * sin(+ ) for = tan(b / a). Thus n would have to be at least 3 since sin(+ ) is at most 1. Also, |n| needs to be at least 3 would be more correct. « Last Edit: Oct 22nd, 2008, 12:50pm by teekyman » IP Logged Michael Dagg Senior Riddler     Gender: Posts: 500 Re: Trig Equation   « Reply #8 on: Oct 23rd, 2008, 1:09pm » Quote Modify One doesn't see that identity all that often.   Also, with a little calculus you can show that the   range of the function  f(x) = (sqrt 7 - 2 sin x)/cos x   is the complement of the open interval  (-sqrt 3,sqrt 3)  . « Last Edit: Oct 23rd, 2008, 1:13pm by Michael Dagg » IP Logged Regards, Michael Dagg Pages: 1  Reply Notify of replies Send Topic Print Forum Jump: ----------------------------- riddles -----------------------------  - easy => medium   - hard   - what am i   - what happened   - microsoft   - cs   - putnam exam (pure math)   - suggestions, help, and FAQ   - general problem-solving / chatting / whatever ----------------------------- general -----------------------------  - guestbook   - truth   - complex analysis   - wanted   - psychology   - chinese « Previous topic | Next topic »

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