Question

the equation cosx=x has a solution in what interval?...the answer is given as [0,pi/2] can someone please explain why?? thnks

Answer 1

That is not the correct answer. Any real number, positive or negative, has a cosine.

You do not even encounter the full range of cosine values when you limit the domain to [0,pi/2]

I suspect you may be using a substandard text or instructor

Answer 2

its not just cosx...its cosx=x

Answer 3

My mistake. I apologize for misreadng the problem.

cosx is confined to the range -1 to 1. Any solutions must first of all be within -1 < x < 1. In the x region -1 to 0, -57.3 to 0 degrees, cos x is positive so there can be no solution for negative x. There is also no solution for x > 1. The only solution that exists is around 0.738. They are correct in saying that the solution is in the domain [0,pi/2], but actually they could have better said it was between 0.73 and 0.74.

To state that [0,pi/2] is the only interval where a solution exists is incorrect and arbitrary. The solution clearly could not be beyond x = 1.

Your confusion about their stated answer is justified