MHB Find zeros f(x)=(x/100)-sin(x)

[karush]

$f(x)=(x/100)-sin(x)$
Find the zeros

Thot my TI was going to melt trying to solve this

 

[mathmari]

$f(x)=0 \Rightarrow \sin x =\frac{x}{100}$

Since $|\sin x| \leq 1$ we conclude that $\left | \frac{x}{100} \right | \leq 1 \Rightarrow |x| \leq 100 \Rightarrow -100 \leq x \leq 100$.

At each period of $\sin x$, the line $y=\frac{x}{100}$ will intersect the curve $y=\sin x$ twice.
Wolfram|Alpha Widget: Math Help Boards: Graph Plotter

From $0$ to $100$ there are $\frac{100}{2\pi}\approx 16$ periods. So, from $0$ to $100$ there are $2 \cdot 16=32$ intersection points.

Similarily, from $-100$to $0$ there are $32$ intersection points.

So, in total there are $32+32-1=63$ (we have count the point $0$ twice) intersection points.

So, the function $f(x)$ has $63$ roots.

 

[Prove It]

$f(x)=(x/100)-sin(x)$
Find the zeros

Thot my TI was going to melt trying to solve this

You aren't going to be able to get exact solutions, but your TI should still be able to give you approximate ones. Make sure you're in either Auto or Approx mode, and then type in

solve( x/100 = sin(x) , x)

 

[karush]

That was amazing, i didn't know how to set up the periods
MHB always out does the textbooks
Much thanks