We can see values of angles in degrees first
[tex] \frac{5\pi}{6} = \frac{5 \times 180}{6}= \frac{900}{6} [/tex] = 150°
Similarly
[tex] \frac{5\pi}{3} = \frac{5 \times 180}{3}= \frac{900}{3} [/tex] = 300°
Now reference angle means positive acute angle they will have
As we can see in attachment 150° lies in second quadrant so its reference angle will be 180°-150° = 30° from x axis line as shown.
Where as angle 300° lies in fourth quadrant so its reference angle will be 360° - 300° = 60° from x axis as shown. So clearly both reference angles are different . So 1st choice " angles donot have same reference angle" best explains it
Choice (2) and (3) are incorrect as tan is positive only in first and third quadrants and angle 300° is in fourth quadrant.
since angle 150° is in second quadrant and 300° is in fourth quadrant so both will have same negative sign so choice (4) is not correct.
So final ansewr is choice (1) "the angles donot have same reference angle"
