Trigonometric equation problem.

Question

Simply and shortly how do I show that this $33 = 33 + 5 \cos(720\cdot t)$ is equal to this $720 \cdot t = 90.$

Thank you for your help.

Answer 1

$$ 33 = 33 + 5\cos(720t) $$

$$ \Leftrightarrow \cos(720t) = 0 $$

$$ \Leftrightarrow 720t = \frac{\pi}{2} + k\pi = 90 ^{\circ} + k \cdot 180^{\circ} \qquad k \in \mathbb{Z}$$

Simply choose $k = 0$