Find the size of angle $t$. Give your answer in degrees $\left(^{\circ}\right)$. Not drawn accurately

Step 1 ：\(\cos t = \cos \left( \frac{180t}{\pi} \right)^\circ\)

Step 2 ：Either \(t + \frac{180t}{\pi} = 360^\circ k\) or \(t - \frac{180t}{\pi} = 360^\circ k\)

Step 3 ：From the first equation, \(t = \frac{360^\circ \pi k}{\pi + 180}\)

Step 4 ：The smallest positive real number of this form is \(\frac{360 \pi}{\pi + 180}\)

Step 5 ：From the second equation, \(t = \frac{360^\circ \pi k}{\pi - 180}\)

Step 6 ：The smallest positive real number of this form is \(\frac{360 \pi}{180 - \pi}\)

Step 7 ：Therefore, \(t = \frac{360 \pi}{\pi + 180} \approx 6.175\)

Step 8 ：\(\lfloor t \rfloor = \boxed{6}\)