Solving the Equation: sinx - x/2 = 0

[sporus]

Homework Statement

sinx -x/2= 0

Homework Equations

The Attempt at a Solution

i don't even know where to start

 

[Mentallic]

Well if it asked you just, \sin(\theta)=0 what would be your answer for \theta?

 

[sporus]

i know that the answer is zero, but i might not get full marks if i don't do it algebraically

 

[Mentallic]

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?

 

[vela]

Are you trying to find all x for which sin x = x/2? You can't solve that algebraically.

 

[Mentallic]

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.

 

[ehild]

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

x_k+1=2 sin(x_k).ehild

 

[sporus]

thanks. plotting sinx - x/2 is a bit hard so i plotted sinx and x/2 and found the intersection point.