Answer:
First option:
The angles do not have the same reference angle.
Explanation:
1.) 5π/6=(5π+π-π)/6=(6π-π)/6=6π/6-π/6=π-π/6 is in the second quadrant. The reference angle is π/6. Tangent is negative in the second quadrant, then second option is incorrect.
2.) 5π/3=(5π+π-π)/3=(6π-π)/3=6π/3-π/3=2π-π/3 is in the fourth quadrant. The reference angle is π/3. Tangent is negative in the fourth quadrant, then third option is incorrect.
3.) Both angles 5π/6 and 5π/3 have the same sign (Both are positive) , then fourth option is incorrect.
4.) The angles do not have the same reference angle (π/6 vs. π/3), then first option is correct.