Question

you are given the point (1,π/2) in polar coordinates. find another pair of polar coordinates for this point such that r>0 and 2π≤θ<4π

Answer 1

Another set of polar coordinates for the point (1, π/2) with r > 0 and 2π ≤ θ < 4π is (1, 5π/2).

Step-by-step explanation:

The student is given a point in polar coordinates (1, π/2), and they need to find another pair of coordinates for the same point with positive radial coordinate r and an angle θ such that 2π ≤ θ < 4π. Since the radius is positive and equal to 1, we only need to adjust the angle. To find a different angle that represents the same point, we can add 2π to the given angle because angles in polar coordinates are periodic with a period of 2π. Thus, adding 2π to π/2 gives us π/2 + 2π = 5π/2, which is between 2π and 4π. Therefore, another set of polar coordinates for the point (1, π/2) with r > 0 and angle in the specified range is (1, 5π/2).

Answer 2

Recall that x radians is the same as
`x+2\pi k` radians where k is an integer.

So, an equivalent point to
`(1,(\pi)/(2))` where r>0 and
`2\pi\leq \theta\leq 4\pi` is
`(1,(5\pi)/(2))`.