Question

Which of the following best explains why tan(5pi/6) doesn't equal tan(5pi/3)

1. The angles do not have the same reference angle.
2. Tangent is positive in the second quadrant and negative in the fourth quadrant
3. Tangent is negative in the second quadrant and positive in the fourth quadrant
4. The angles do not have the same reference angle or the same sign

Answer 1

The angles do not have the same reference angle.

Explanation:

2π = 360°

π = 180°

5π/6 =
`(5 * 180)/(6)` = 150° (The reference angle here is 180° - 150° = 30°

5π/3 =
`(5 * 180)/(3)` = 300° (The reference angle here is 360° - 300° = 60°)

The reference angles are not the same and so the value of their tangents are not equal.

Answer 2

1. The angles do not have the same reference angle

Explanation:

The angles are in the 2nd and 4th quadrants, so both have tangents with a negative sign. (This eliminates choices 2, 3, 4.)

The angles do not have the same reference angle.

_____

5π/6 has a reference angle of π/6.

5π/3 has a reference angle of π/3.