What is   $\frac{3\pi }{2}$   radians in degrees?

The correct option is 270°.

To convert an angle from radians to degrees, we use the conversion factor based on the relationship that $\pi$ radians is equal to 180 degrees.

The conversion formula is:

$\text{Angle in degrees}=\text{Angle in radians}\times \frac{180°}{\pi }$

Given the angle in radians as $\frac{3\pi }{2}$, we substitute it into the formula:

$\text{Angle in degrees}=\frac{3\pi }{2}\times \frac{180°}{\pi }$

Now, simplify the expression step-by-step:
1. Cancel out $\pi$ from both the numerator and denominator:
$=\frac{3}{2}\times 180°$
2. Divide 180° by 2:
$=3\times 90°$
3. Multiply 3 by 90°:
$=270°$

Therefore, $\frac{3\pi }{2}$ radians is equal to 270°.