You may be better off without using trig. For a function having bumps near $a,b$ with their heights controlled by $k1,k2$, I found that $f(x)=\frac{k1(x-a)^2+k2(x-b)^2}{x^4+1}$ works well. For my test case I used values of $a,b$ which were negatives of each other, which you can do by using the average of where you want the bumps, and shifting the inputs. And the larger value of $k1,k2$ went with the shorter hump.
When one puts this function into a derivative formula in order to find the exact location of local maxes, one has to solve a fifth degree equation to get the $x$ coordinates where the maxes actually occur. Seems these are only "near" the points $a,b$ used in making up the function. And of course this function is not periodic, since it dies off away from zero.
If you want a trig version, it looks like you can use $f(x)=a \sin^2{x}+b \sin^2{2x}+c \sin^2{4x}-2a/\pi$ but only graph it from $0$ to $\pi/2$. Outside that range it gets wierd, not looking like a double hump. For this one I don't know how to fiddle around with $a,b,c$ to control the hump sizes, but at least in the few cases I tried I got humps of different sizes.