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.