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wu :: forums    riddles    medium (Moderators: Eigenray, Grimbal, Icarus, william wu, ThudnBlunder, towr, SMQ)    Trigonometric equation « Previous topic | Next topic » Pages: 1  Reply Notify of replies Send Topic Print    Author  Topic: Trigonometric equation  (Read 962 times) wonderful Full Member     Posts: 203 Trigonometric equation   « on: Jun 15th, 2008, 6:56pm » Quote Modify Solve: (sinx)^2 + (siny)^2 +[sin(x+y)]^2 = 9/4   Have A Great Day! IP Logged Barukh Uberpuzzler     Gender: Posts: 2276 Re: Trigonometric equation   « Reply #1 on: Jun 16th, 2008, 11:07am » Quote Modify I think calculus may help here. IP Logged Eigenray wu::riddles Moderator Uberpuzzler     Gender: Posts: 1948 Re: Trigonometric equation   « Reply #2 on: Jun 16th, 2008, 11:27am » Quote Modify I think triangles should help too, but I suck at geometry. IP Logged Aryabhatta Uberpuzzler     Gender: Posts: 1321 Re: Trigonometric equation   « Reply #3 on: Jun 16th, 2008, 3:13pm » Quote Modify Pure algebraic manipulations will do too:     Note that using 1 - 2sin2(x) = cos(2x), we can rewrite the equation as   cos (2x) + cos(2y) + cos(2x+2y) = -3/2   i.e 2 cos(x+y)cos(x-y) + 2cos2(x+y) = -1/2   ie   1 + 4 cos(x+y)cos(x-y) + 4 cos2(x+y) = 0   i.e   sin2(x-y) + (cos(x-y) + 2cos(x+y))2 = 0   Thus sin(x-y) = 0 and   cos(x-y) +2 cos(x+y) = 0.   The solution set should follow easily now. IP Logged wonderful Full Member     Posts: 203 Re: Trigonometric equation   « Reply #4 on: Jun 16th, 2008, 4:43pm » Quote Modify Aryabhatta is correct.   Have A Great Day! IP Logged Sir Col Uberpuzzler impudens simia et macrologus profundus fabulae     Gender: Posts: 1825 Re: Trigonometric equation   « Reply #5 on: Jun 16th, 2008, 11:38pm » Quote Modify Stunning, Aryabhatta!   IP Logged mathschallenge.net / projecteuler.net Aryabhatta Uberpuzzler     Gender: Posts: 1321 Re: Trigonometric equation   « Reply #6 on: Jun 18th, 2008, 7:20pm » Quote Modify Thanks   I guess we can also do something using complex numbers... IP Logged 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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