sin(t)≥\/3/2 inequation

Given the inequality:
$$\sin{\left(t \right)} \geq \frac{3}{2}$$
To solve this inequality, we must first solve the corresponding equation:
$$\sin{\left(t \right)} = \frac{3}{2}$$
Solve:
Given the equation
$$\sin{\left(t \right)} = \frac{3}{2}$$
transform
$$\sin{\left(t \right)} - \frac{3}{2} = 0$$
$$\sin{\left(t \right)} - \frac{3}{2} = 0$$
Do replacement
$$w = \sin{\left(t \right)}$$
Move free summands (without w)
from left part to right part, we given:
$$w = \frac{3}{2}$$
We get the answer: w = 3/2
do backward replacement
$$\sin{\left(t \right)} = w$$
substitute w:
$$x_{1} = 1.5707963267949 + 0.962423650119207 i$$
$$x_{2} = 1.5707963267949 - 0.962423650119207 i$$
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

$$\sin{\left(t \right)} \geq \frac{3}{2}$$

sin(t) >= 3/2

so the inequality has no solutions