Quadratic equation to find max and min

[Lifeforbetter]

Also, if you ever need, $- \sqrt{a^2+b^2} \leq acos(\theta)+bsin(\theta) \leq \sqrt{a^2+b^2}$

How about this?

 

[Pi-is-3]

How about this?

Do you mean the proof? You can prove it through Lagrange multipliers, or their is a trigonometrical proof too. For the Lagrange multipliers proof, your optimization function is $acos(\theta)+bsin(\theta)$ and restrain function is $cos^2(\theta)+sin^2(\theta)=1$.