2 Trig Equations Answer one or the other is fine

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Discussion Overview

The discussion revolves around solving two trigonometric equations: Tan(x) = 3 tan(x/2) and sin(3x)cos(x) + cos(3x)sin(x) = 1, both within the interval 0 < x < 2π. Participants explore methods for finding solutions and share insights on the equations' properties.

Discussion Character

  • Homework-related
  • Exploratory
  • Technical explanation

Main Points Raised

  • One participant suggests using a graphical method to find intersections of the two equations, implying that visual insights can aid in solving them.
  • Another participant references a 1954 mathematics book that contains exact trigonometric relationships, indicating that these relationships might be useful for solving the equations.
  • A different participant identifies the second equation as resembling an addition theorem, proposing to find suitable angles alpha and beta to facilitate the solution.

Areas of Agreement / Disagreement

Participants have not reached a consensus on the best method for solving the equations, and multiple approaches are being discussed without resolution.

Contextual Notes

Some methods mentioned may depend on specific assumptions about the equations, and the effectiveness of graphical versus analytical approaches remains unresolved.

BuffaloSoulja
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Tan(x)=3 tan(x/2) solve where 0<x<2pi?


sin3xcosx+cos3xsinx=1, where 0<x<2pi?



tried a long time...
 
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Hiya
what methods have you tried? A graphical method often leads to insights - plot the 2 graphs and see where they intersect. Then look for the reasons why and hey presto! the answer.
 
My old (1954) CRC Mathematics Tables book has exact trig relationships for tan x, tan 2x, and tan 3x. Also sin x, sin 2x, sin 3x, sin 4x and sin 5x. Also cosines. (page 344)
Bob S
 
BuffaloSoulja said:
Tan(x)=3 tan(x/2) solve where 0<x<2pi?


sin3xcosx+cos3xsinx=1, where 0<x<2pi?



tried a long time...
Hello BuffaloSoulja
The second looks very much like an addition theorem:
sin(alpha+beta)=sin(alpha)cos(beta)+cos(alpha)sin(beta)
find alpha and beta and make the solution.
greetings Janm
 

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