I am currently struggling with how to answer this question:
"Consider the planar curve $y = a\sin(bx)$ where $a, b$ are non-zero real numbers. Find constants $A$ and $B$ so that $A \le k \le B$ for all $x$, where $k$ is the curvature at $x$. These constants will be dependent on $a, b$"
I used the definition for curvature for a planar curve to get
$$k = \frac{|ab^2\sin(bx)|}{(1+(ab\cos(bx))^2)^{3/2}}$$
I know $\cos(bx)$ and $\sin(bx)$ oscillate but the curvature is always even, so I don't know what to do from here. Any help would be appreciated.