Have you tried graphing the functions? The answershould then be obvious.Spoiler:
I know the graphs intersect three times, one at (0,0) and the other 2 points are reflected about the y-axis. Is there a solution for this exercise? I can't think of any of these points where a value of X is less than its sin value. And also, is there any way I can solve for the other 2 points algebraically? Because I've been approximating and it seems my approximates aren't that good...
Thanks in advance guys, I appreciate it.
Alright guys, thanks for the help. I understand the inequality now.
Just one more question: Is there any way I can get the exact values by algebraic methods? If I try to do it graphically, my approximations are not as nearly as accurate. I know the graphs intersect 3 times and one is (0,0), but how would I determine the other points without approximating? Because frankly, my graphing software sucks. ><
Ah, it was just a mistake with my software then. But I have other questions where there is more than 1 intersection, and my approximation with the software is not that good.
So how would I be able to solve for the exact points of intersection? Ex: finding the 4 points where Thanks for all the help, by the way.
The Newton-Raphson formula is
It's an iterative process. is a first guess at a solution.
Then is the calculated first approximation. will be much closer, as will
Take an initial guess at the next root of say .
Then
Use the result as in the 2nd iteration, which should be enough.
Use as an initial guess for the 3rd root of