Use the intermediate value theorem to determine whether the following the equation has a solution or not. If so, then use a graphing calculator to solve the equation.

cosx=x

Please help me understand this!

Question

Use the intermediate value theorem to determine whether the following the equation has a solution or not. If so, then use a graphing calculator to solve the equation. 

cosx=x

Please help me understand this!

anonymous · Answer

From $-\pi$ to $\pi$, $\cos(x)$ ranges from $-1$ to $1$ to $-1$ again.

anonymous · Answer

They probably want you to use this fact.

anonymous · Answer

To be more specific, $\cos(0) = 1$ and $\cos(\pi)=0$.

nincompoop · Answer

this is so vague that you have the freedom to choose what your value for c is going to be

anonymous · Answer

Then, what would x  be approx.?

anonymous · Answer

Indeed, it is very vague and I think it's vague-ness is throwing me off.

anonymous · Answer

Okay, here is another idea.  Let $f(x)=\cos(x)-x$.  Use intermediate value theorem to find out if there is any interval where $f(x)=0$.

nincompoop · Answer

that makes it easier, @wio

nincompoop · Answer

but you should provide the interval as well

anonymous · Answer

Same as before.  $f(0) = 1$ and $f(\pi) = -\pi$.  We know $f(x)$ is continuous so it mus go through $0$.

nincompoop · Answer

thank you, that's all folks

anonymous · Answer

Did you use a calculator to come to that conclusion or was that knowledge you knew before hand?

anonymous · Answer

I actually understand trigonometry, so I know certain values of $\cos(x)$.

nincompoop · Answer

wio is a human calculator

anonymous · Answer

attachment

anonymous · Answer

I understand trig functions but this problem seems like it requires more than one answer and I'm still so confused.

zepdrix · Answer

So you've used the IVT to determine that `yes` a solution exists.
The next part is just to use a calculator of some sort to approximate the solution.

If you don't have a graphing calculator, use Wolfram as a nice resource.