What Values Make f(23,x) Equal to f(33,x) for 100<x<200 Degrees?

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SUMMARY

The discussion focuses on the mathematical function f(n,x) defined as the ratio of the sum of sine functions to the sum of cosine functions, specifically f(23,x) and f(33,x). Participants are tasked with finding the values of x, within the range of 100 to 200 degrees, that satisfy the equation f(23,x) = f(33,x). Various methods, including plugging in values and applying De Moivre's theorem, were attempted but yielded no conclusive results. The need for a systematic approach to solve the equation is emphasized.

PREREQUISITES
  • Understanding of trigonometric functions, specifically sine and cosine.
  • Familiarity with the concept of function ratios.
  • Knowledge of De Moivre's theorem and its applications.
  • Ability to manipulate and solve equations involving trigonometric identities.
NEXT STEPS
  • Explore the properties of trigonometric sums and their simplifications.
  • Study the application of De Moivre's theorem in solving trigonometric equations.
  • Investigate numerical methods for solving equations within specified ranges.
  • Learn about the behavior of the function f(n,x) for various values of n and x.
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Mathematics students, educators, and anyone interested in solving trigonometric equations or exploring the properties of sine and cosine functions in applied contexts.

newchie
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Homework Statement


consider the function
f(n,x) = (sinx+sin2x+sin3x +...+sin(n-1)x+sinnx)/)cosx+cos2x+cos3x+...+cos(n-1)x+cosnx)
Find the sum of all values for which f(23,x) = f(33,x)where x is measured in degrees from 100<x<200



Homework Equations


you get obviously tanx+tan2x...
not sure where to go other than pluggin in values


The Attempt at a Solution


Plugging in values, testing cases trying different methods including demoivres, but doesent help. Help is appreciated!
 
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newchie said:

Homework Statement


consider the function
f(n,x) = (sinx+sin2x+sin3x +...+sin(n-1)x+sinnx)/(cosx+cos2x+cos3x+...+cos(n-1)x+cosnx)
Find the sum of all values for which f(23,x) = f(33,x)where x is measured in degrees from 100<x<200

Homework Equations


you get obviously tanx+tan2x...
not sure where to go other than pluggin in values

The Attempt at a Solution


Plugging in values, testing cases trying different methods including demoivres, but doesent help. Help is appreciated!
You do not get tan(x)+tan(2x)+ ...

\displaystyle \frac{a+b+c}{e+f+g}\ne\frac{a}{e}+\frac{b}{f}+ \frac{c}{g}\ \ \
 
SammyS said:
You do not get tan(x)+tan(2x)+ ...

\displaystyle \frac{a+b+c}{e+f+g}\ne\frac{a}{e}+\frac{b}{f}+ \frac{c}{g}\ \ \

ah yes woops, i misread hehe, anyways do you have an approach on this problem
 

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