Which of the following best explains why tan 5pi/6 does not equal to tan 5pi/3?
a. the angles do not have the same reference angle.
b. tangent is positive in the second quadrant and negative in the fourth quadrant.
c. tangent is negative in the second quadrant and positive in the fourth quadrant.
d. the angles do not have the same reference angle or the same sign.

Option A. The angles do not have the same reference angle.

Explanation:

1) Angle 5π / 3 radians:

2) Angle 5π / 6 radians:

3) Conclusion:

Note that the tangent is negative in both second and fourth quadrants.

The correct option is A.

Step-by-step explanation:

The first expression is,

The reference angle is . In second quadrant the sign of tangent is negative.

The second expression is,

The reference angle is . In fourth quadrant the sign of tangent is negative.

Since the sign are same but the reference angle is are different, therefore the correct option is A.

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distance covered by pamela in 9 l of fuel = 99km

let us apply unitary method here.

distance covered by pamela in 1 l of fuel =99/9 =11 km

now let us find distance covered by pamela if she has 12 l of fuel.

distance covered in 12 l = distance covered in 1 l of fuel * 12

we know that distance covered by here in 1 l is 11 km.

so distance covered in 12 l of fuel = 11*12 = 132 km.