sint≤12 inequation

Given the inequality:
$$\sin{\left(t \right)} \leq 12$$
To solve this inequality, we must first solve the corresponding equation:
$$\sin{\left(t \right)} = 12$$
Solve:
Given the equation
$$\sin{\left(t \right)} = 12$$
transform
$$\sin{\left(t \right)} - 12 = 0$$
$$\sin{\left(t \right)} - 12 = 0$$
Do replacement
$$w = \sin{\left(t \right)}$$
Move free summands (without w)
from left part to right part, we given:
$$w = 12$$
We get the answer: w = 12
do backward replacement
$$\sin{\left(t \right)} = w$$
substitute w:
$$x_{1} = 1.5707963267949 + 3.17631318059166 i$$
$$x_{2} = 1.5707963267949 - 3.17631318059166 i$$
Exclude the complex solutions:
This equation has no roots,
this inequality is executed for any x value or has no solutions
check it
subtitute random point x, for example

x0 = 0

$$\sin{\left(t \right)} \leq 12$$

sin(t) <= 12

so the inequality has no solutions