두 삼각함수의 교점

$\displaystyle 0 < k < \frac{2}{t}$에서 $0 < tk \pi < 2 \pi$ $f \left( k \right) = 3 k$에서 $\displaystyle \sin \left( tk \pi \right) = \sqrt{3} k > 0$이고 $g \left( k \right) = 3 k$에서 $\cos \left( tk \pi \right) = - k < 0$이므로 $\displaystyle \frac{\pi}{2} < tk \pi < \pi$ $f \left( k \right) = g \left( k \right)$에서 $\displaystyle \tan \left( tk \pi \right) = - \sqrt{3}$이므로 $\displaystyle tk \pi = \frac{2}{3} \pi$, $\displaystyle tk = \frac{2}{3}$ $f \left( k \right) = 3 k$에서 $\displaystyle \sqrt{3} \sin \frac{2}{3} \pi = \frac{3}{2} = 3 k$이므로 $\displaystyle k = \frac{1}{2}$, $\displaystyle t = \frac{4}{3}$ 따라서 $\displaystyle 60 \left( t + k \right) = 60 \left( \frac{4}{3} + \frac{1}{2} \right) = 110$