Question

Which of the following best explains why

Answer 1

We can see values of angles in degrees first

$\frac{5\pi}{6} = \frac{5 \times 180}{6}= \frac{900}{6}$ = 150°

Similarly

$\frac{5\pi}{3} = \frac{5 \times 180}{3}= \frac{900}{3}$ = 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"