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.

If $f(x) = 5|\sin x| + 12 |\cos x|$, then
\begin{align*}
f(x) &= \sqrt{f(x)^2} \\
&= \sqrt{25 \sin^2 x + 144 \cos^2 x + 60 |\sin x \cos x|} \\
&= \sqrt{25 + (144 - 25) \cos^2 x + 60 |\sin x \cos x|} \\
&\ge 5
\end{align*}
with equality obtained when $\cos x = 0$.
