How Do You Determine the Number of Solutions for sin(x) = |x|/10?

[utkarshakash]

Homework Statement

The number of solutions of the equation sin x = |x|/10

Homework Equations

The Attempt at a Solution

When x>0
10sinx-x=0
When x<0
10sinx+x=0

But how do I solve the above equations?

 

[Ray Vickson]

Homework Statement

The number of solutions of the equation sin x = |x|/10

Homework Equations

The Attempt at a Solution

When x>0
10sinx-x=0
When x<0
10sinx+x=0

But how do I solve the above equations?

Draw a graph of sin(x) and |x|/10; this will tell you the number of solutions, and will also give you a very rough idea of where the solutions lie.

 

[Joffan]

IF you only need the number of solutions, and not the solutions themselves, a graph should almost be enough. If you need a little more reasoning, consider:
a) the maximum value of sine
b) the sign of |x|/10
b) the number of possible crossings per sine period.

 

[haruspex]

As a useful check, you should be able to see quickly whether the number of solutions with x > 0 is even or odd.

 

[utkarshakash]

Draw a graph of sin(x) and |x|/10; this will tell you the number of solutions, and will also give you a very rough idea of where the solutions lie.

Thanks