Find the size of angle $t$. Give your answer in degrees $\left(^{\circ}\right)$.

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Answer

$\lfloor t \rfloor = \boxed{6}$

Steps

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 ：$\lfloor t \rfloor = \boxed{6}$