삼각함수 최대최소

$\displaystyle x = \theta + \frac{3}{4} \pi$라 하면 $\displaystyle f \left( \theta + \frac{3}{4} \pi \right) = \cos ^{2} \theta - \cos \left( \theta + \frac{\pi}{2} \right) + k$ $= \cos ^{2} \theta + \sin \theta + k$ $= 1 - \sin ^{2} \theta + \sin \theta + k$ $\displaystyle = - \left( \sin \theta - \frac{1}{2} \right) ^{2} + k + \frac{5}{4}$ 최댓값은 $\displaystyle k + \frac{5}{4} = 3$, $\displaystyle k = \frac{7}{4}$ 최솟값은 $\sin \theta = - 1$일 때, $\displaystyle m = \frac{3}{4}$ $\displaystyle k + m = \frac{7}{4} + \frac{3}{4} = \frac{5}{2}$