If $t$ is in degrees (should be radians imho), then your inequality isi tried to work out the following 15cos30t+50<25
$15\cos(30t) + \color{red}{35} < 25$
solving this inequality yields $4.4 < t < 7.6$ in the first period of 12 months
... then maybe you should learn how.
https://www.khanacademy.org/math/tri...unction-graphs