Why is a Non-Zero Root Used in Newton's Method for Sin(x) = x^2?

[Miike012]

Question:
Use Newtons method to approximate the indicated root of the equation correct to six decimal places.

The positive root of sin(x) = x^2

The answer is ...0.876726

Why did they pick this when the obvious root is 0?

Sin(0) = (0)^2 = 0

 

[Simon Bridge]

There are two roots - they want you to find the other one.
The one that it actually helps to use Newton's method for.

 

[Pablo Antuna]

Yes, they wouldn't ask you to use Newton's Method if they only wanted the trivial root. Try to start with a first approximation that is near the root. I'd try 1.