What is the Range of $5|\sin x|+12|\cos x|$ What is the Range of $5|\sin x|+12|\cos x|$ ?
I entered the value in desmos.com and getting the range as $[5,13]$.
Using $\sqrt{5^2+12^2} =13$, i am able to get maximum value but not able to find the minimum.

Another possible approach.
For the first quadrant: $5\sin(x) + 12\cos(x) = 13\sin(x + \arccos(\frac{5}{13}))$. Can follow from there for the rest of the quadrants. Can also try alternative forms for arguments in order to adapt to the values of $x$.
