Which of the following polar coordinates describes the same point as the point (5, -pi/6) given in polar coordinates?

a.) (5, pi/6)
b.) (-5, -pi/6)
c.) (5, 5pi/6)
d.) (-5, 5pi/6)
e.) none of these

you can get positive angles from negative by adding 2PI.

What is 2PI-pI/6? Answer 5pi/6

2pi - pi/6 = 11pi/6

that's not one of the choices.
But, 5pi/6 is, and 5pi/6 = 11pi/6 - pi, so switch the radius value of 5 to -5, which flips it through the origin.
So, D
If in doubt, just plot the points.

To find the polar coordinates that describe the same point as (5, -pi/6), we need to consider the distance from the origin (5) and the angle from the positive x-axis (-pi/6).

Since the angle is given as -pi/6, which is in the fourth quadrant, we would need to add pi radians (180 degrees) to the angle to bring it into the first quadrant. Adding pi to -pi/6 gives us 5pi/6.

Therefore, the correct polar coordinates that describe the same point as (5, -pi/6) are (5, 5pi/6).

The correct answer is c.) (5, 5pi/6).

To find the polar coordinates that describe the same point as (5, -pi/6), we need to understand how polar coordinates work.

In polar coordinates, a point is represented by the length of a vector from the origin (known as the magnitude or radius) and the angle the vector makes with the positive x-axis (known as the angle or argument).

In this case, the given point (5, -pi/6) has a magnitude of 5 and an angle of -pi/6.

To determine the polar coordinates that describe the same point, we can keep the same magnitude (5) and find an equivalent angle.

Since the angle -pi/6 is in the fourth quadrant (between pi/2 and pi), we need to add 2pi to find an equivalent angle in the first quadrant.

Adding 2pi to -pi/6 gives us an equivalent angle of (11pi/6).

Thus, the polar coordinates that describe the same point as (5, -pi/6) are (5, 11pi/6).

None of the options provided in the question match this answer, so the correct answer is e.) none of these.