To solve the equation $\cos(x) = 0$ for $x$ in degrees, we can express the solution as:

where $n$ is any integer.

The cosine function equals zero at specific angles on the unit circle. Notably, in degrees, these angles are $90^\circ$ and $270^\circ$ within a complete cycle of $360^\circ$. Since the cosine function is periodic with a period of $360^\circ$, it repeats its values every $360^\circ$.

To generalize the solution, we can utilize the formula $x = 90^\circ + 180^\circ n$. This expression encompasses all angles where the cosine function equals zero. For instance:

• When $n = 0$, we find $x = 90^\circ$.
• When $n = 1$, we obtain $x = 270^\circ$.
• When $n = -1$, we calculate $x = -90^\circ$, which is equivalent to $270^\circ$ in the standard range of $0^\circ$ to $360^\circ$.

In summary, the angles where $\cos(x) = 0$ can be represented as $90^\circ$, $270^\circ$, $450^\circ$, and so forth. This can be succinctly expressed as $90^\circ + 180^\circ n$ for any integer $n$. This pattern continues indefinitely in both the positive and negative directions, thus covering all possible solutions.