Question

is there a value of x where cos(x)=x

Answer 1

Yeah, there is.

Answer 2

Can you explain?

Answer 3

Newton's method?

Answer 4

You basically have to find the root of \[
\cos(x)-x=0
\]

Answer 5

Think about it this way...
As \(x\) goes from \(0\) to \(\pi\), \(\cos x\) goes from \(1\) to \(0\).

Answer 6

And this happens in a one-to-one manner.

Answer 7

Oh ok that makes sense. Thank you so much this really helps

Answer 8

So they have to meet at some point.

Answer 9

Should maybe say as \(x\) goes from \(0\) to \(\pi/2\)

Answer 10

Although this wouldn't be very easy to solve algebraically, but one thing you know for sure is that this will have 1 solution since the line y = x and the curve y = cos(x) have to intersect at some point.

@skater93

Answer 11

It has 2 solutions, because the negative case is symmetrically identical.

Answer 12

at least

Answer 13

There is a single intersection point?