Question

Which values for theta have the same reference angles

Answer 1

The 4th selection is the correct one.

_____
The fact that denominators are different eliminates all the other choices.

Answer 2

Answer: The correct option is 4.

Explanation:

If the reference angle is $\theta$ then the angles $\pi-\theta$,$\pi+\theta$ and $2\pi-\theta$ have same reference angle.

If the reference angle is $\frac{\pi}{4}$, then the following angles have same reference angles.

$\pi-\frac{\pi}{4}=\frac{3\pi}{4}$

$\pi+\frac{\pi}{4}=\frac{5\pi}{4}$

$2\pi-\frac{\pi}{4}=\frac{7\pi}{4}$

Since the angles $\frac{\pi}{4},\frac{3\pi}{4},\frac{7\pi}{4}$ have same reference angle $\frac{\pi}{4}$, therefore the correct option is 4.

In other options, the denominators terms are not equal, therefore the given angle can not be represent in the form of $\pi-\theta$,$\pi+\theta$ and $2\pi-\theta$, so the remaining options are incorrect.