The condition $\pi < \theta < \frac{3\pi}{2}$ specifies the interval for $\theta$, which is the range of angles in radians between $\pi$ and $\frac{3\pi}{2}$. This interval corresponds to the third quadrant of the unit circle.

Here’s a breakdown:

• $\pi$ (or 180°) is the angle on the negative x-axis.
• $\frac{3\pi}{2}$ (or 270°) is the angle on the negative y-axis.
• This means $\theta$ is between 180° and 270° (or between $\pi$ and $\frac{3\pi}{2}$ radians), so the angle lies in the third quadrant of the unit circle, where both sine and cosine values are negative.

If you're working with a trigonometric equation, you would use this range to determine the possible values of $\theta$ that satisfy the equation.

Do you need help with a specific trigonometric equation or expression involving this interval?