How to find the number of times a weather station registered a certain temperature? The problem is as follows:

The temperature in the city of Daegu on March 1st, 2020 is given by:
$15+5\sin\left(\frac{\pi t}{12}+\frac{\pi}{2}\right)$ in celcius, where
$t\in [0,24]$. Assume $t$ is the time elapsed in hours from midnight.
Using this information. Find how many times the temperature of the
city was measured to be $17.5$ celcius.

What I've attempted to do in order to solve this problem isn't much. What I arrived was this:
$$15+5\sin\left(\frac{\pi t}{12}+\frac{\pi}{2}\right)=17.5$$
Then this is reduced to:
$$\sin\left(\frac{\pi t}{12}+\frac{\pi}{2}\right)=\frac{1}{2}$$
But now what? I could use the inverse sine function as:
$$\frac{\pi t}{12}=\sin ^{-1}\left(\frac{1}{2}\right)-\frac{\pi}{2}$$
But from looking at this effort, I don't seem this would help me to get the value of $t$, needless to say. Assuming that I could get that value. How can I get how many times that temperature was attained?. Therefore I need assistance in this problem.
 A: from $$\sin\left(\frac{\pi t}{12} + \frac{\pi} 2\right)=\frac12$$
We have $$\frac{\pi t}{12} + \frac{\pi}2 = k\pi + (-1)^k\cdot \frac{\pi}6, k \in \mathbb{Z}$$
Simplifying, we have
$$t + 6 = 12k + 2(-1)^k, k \in \mathbb{Z}$$
$$t  = 12k - 6 + 2(-1)^k, k \in \mathbb{Z}$$
Now, we have the restriction of $t$ should be in $[0, 24]$.
When $k=0,$ we have $t<0$
When $k=1$, we have $t=12-6-2=4.$
When $k=2$, we have $t=24-6+2=20$
When $k=3$, we have $t = 36-6-2 > 24$.
Hence the answer is two times.
A: First note that
$$15+5\sin\left(\frac{\pi t}{12}+\frac{\pi}{2}\right)=17.5$$
$$5\sin\left(\frac{\pi t}{12}+\frac{\pi}{2}\right)=\frac52$$
$$\sin\left(\frac{\pi t}{12}+\frac{\pi}{2}\right)=\frac12$$
$$\cos\left(\frac{\pi t}{12}\right)=\frac12$$
Which yields
$$\frac{\pi t_1}{12}=\frac\pi3+2\pi k,\ \mbox{for}\ k\in\mathbb Z$$
$$\frac{\pi t_2}{12}=\frac{5\pi}{3}+2\pi k,\ \mbox{for}\ k\in\mathbb Z$$
Solving for $t_1$ and $t_2$, we have
$$t_1=24k+4,\ \mbox{for}\ k\in\mathbb Z$$
$$t_2=24k+20,\ \mbox{for}\ k\in\mathbb Z$$
The only scenario in which $t_i\in[0, 24]$ is when $k=0$. So now we have
$$0\le t_1=4\le 24$$
$$0\le t_2=20\le 24$$
Therefore on March 1st, 2020, there were two occurrences in which the city of Daegu attained a temperature of $17.5^\circ \mathrm C$.
