Taylor Polynomial approximation

[zjhok2004]

Homework Statement

obtain the number r = √15 -3 as an approximation to the nonzero root of the equation x^2 = sinx by using the cubic Taylor polynomial approximation to sinx

Homework Equations

cubic taylor polynomial of sinx = x- x^3/3!

The Attempt at a Solution

Sinx = x-x^3/3! + E(x)
x^2 = x-x^3/6+ E(x)How do I able to obtain the r?

 

[jbunniii]

In order to get exact equality you need
$$\sin(x) = x - x^3/6 + E(x)$$
where $E(x)$ is the error due to using only two terms. As an approximation, we assume this error to be zero, so we pretend that
$$\sin(x) = x - x^3/6$$
and solve the equation
$$x^2 = x - x^3/6$$

 

[zjhok2004]

In order to get exact equality you need
$$\sin(x) = x - x^3/6 + E(x)$$
where $E(x)$ is the error due to using only two terms. As an approximation, we assume this error to be zero, so we pretend that
$$\sin(x) = x - x^3/6$$
and solve the equation
$$x^2 = x - x^3/6$$

But how do I able to obtain the number r?

 

[jbunniii]

But how do I able to obtain the number r?

As the problem statement says, $r$ is a nonzero root of the equation $x^2 = \sin(x)$. You will find an approximation to this by solving the equation $x^2 = x - x^3/6$.

 

[zjhok2004]

As the problem statement says, $r$ is a nonzero root of the equation $x^2 = \sin(x)$. You will find an approximation to this by solving the equation $x^2 = x - x^3/6$.

Solved, thanks!