sin x=x^2+1?

Question

"Determine the number of (real) solutions. Solve for the intersection points exactly if possible and estimate the points if necessary."

I've graphed it and found that it has no real solutions, but I'm not sure how to find that algebraically

Answer 1

sin(x) is always less than or equal to 1. x^2+1 is always greater than or equal to 1. The only place x^2+1 = 1 is at x=0, therefore the only place sin(x) and x^2+1 can possibly intersect is at x=0. If f(x) = sin x and g(x) = x^2 + 1, if f(0) is not equal to g(0), this equation has no real solutions.

Answer 2

I know you wanted real solutions, but since there aren't any, prehaps you would like a complex one.

x = 0.488 + 0.785i
x = 0.488 - 0.785i