Solving the Equation: sinx - x/2 = 0

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SUMMARY

The equation sin(x) - x/2 = 0 cannot be solved algebraically; numerical methods are required to find the solutions. Participants in the discussion emphasized the importance of plotting the functions sin(x) and x/2 to identify intersection points, which represent the solutions. The iterative method xk+1 = 2 sin(xk) was suggested for approximating the roots. The discussion clarified that solutions exist beyond just x = 0, including an infinite number of solutions within specific intervals.

PREREQUISITES
  • Understanding of trigonometric functions, specifically sine.
  • Familiarity with numerical methods for solving equations.
  • Knowledge of plotting functions on a Cartesian plane.
  • Basic understanding of iteration techniques in mathematics.
NEXT STEPS
  • Learn about numerical methods for root-finding, such as the Newton-Raphson method.
  • Explore graphing tools or software for visualizing functions, like Desmos or GeoGebra.
  • Study the concept of fixed-point iteration and its applications.
  • Investigate the properties of trigonometric equations and their solutions over specified intervals.
USEFUL FOR

Students studying calculus, mathematicians interested in numerical analysis, and educators teaching trigonometric equations and their solutions.

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Homework Statement



sinx -x/2= 0

Homework Equations





The Attempt at a Solution



i don't even know where to start
 
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Well if it asked you just, \sin(\theta)=0 what would be your answer for \theta?
 
i know that the answer is zero, but i might not get full marks if i don't do it algebraically
 
The answer isn't just 0. What about \pi? In fact there are an infinite number of solutions. Did the question say anywhere to find the solutions to this problem for some restricted value of x, say 0\leq x\leq 2\pi?
 
Are you trying to find all x for which sin x = x/2? You can't solve that algebraically.
 
Oh I completely missed the sinx-x/2=0, sorry, I read it as sin(-x/2)=0...

Yes as vela said, you can't solve it algebraically, you'll have to solve it numerically.
 
Plot sin(x)-x/2 (do not forget that x is in radians) and find the approximate x values where it is zero.
Then pick up one of these and try the iteration

xk+1=2 sin(xk).ehild
 
thanks. plotting sinx - x/2 is a bit hard so i plotted sinx and x/2 and found the intersection point.
 

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