Final answer:
To solve the equation 1/sin^2 x = 4 for x between 180° and 270°, the value of x is equal to 210°.
Step-by-step explanation:
To solve for x, which falls between 180° and 270°, we need to start by rearranging the equation:
1/sin^2 x = 4
sin^2 x = 1/4
sin x = ±(1/2)
We know that sin x = 1/2 for angles 30° and 150°, in the first and second quadrants respectively. However, for angles between 180° and 270°, the value of sin x is negative. Therefore, the solution for x in this range is 210°.