Answer
The solution set is $$\{180^\circ+360^\circ n, n\in Z\}$$
Work Step by Step
$$\cos\theta+1=0$$
1) Solve the equation over the interval $[0^\circ,360^\circ)$
$$\cos\theta+1=0$$
$$\cos\theta=-1$$
Look at the unit circle, we find that over the interval $[0^\circ, 360^\circ)$, there is only one value of $\theta$ which $\cos\theta=-1$, which is $\theta=180^\circ$.
Therefore, $$\theta=\{180^\circ\}$$
2) Solve the equation for all solutions
To find all solutions, we add the integer multiples of the period of cosine function, which is $360^\circ$ to each solution found in step 1.
In detail, there is one solution found in step 1, $180^\circ$, so it will be written as $\theta=180^\circ+360^\circ n (n\in Z)$.
In other words, the solution set is $$\{180^\circ+360^\circ n, n\in Z\}$$
