Question

PRE CALC PEOPLE HELP PLSSSSS

Find three additional polar representations of the point (2, 3π/4)
using −2 < < 2.
(r, ) = smallest value?
(r, ) = ?
(r, ) = largest value?

Answer 1

To find three additional polar representations of the point (2, 3π/4), we can add or subtract 2πk to the angle, where k is an integer. Using this method, we get:

(2, -5π/4) - subtract 2π

(2, 11π/4) - add 2π

(2, -3π/4) - subtract 2π

To find the smallest and largest values of the angle, we need to consider the interval −2π < θ < 2π. The given angle of 3π/4 lies in the second quadrant. Adding or subtracting 2π to this angle will give us angles in the third and fourth quadrants. Therefore, the smallest value of the angle is −3π/4, and the largest value is 5π/4. Thus, the polar representations are:

(2, 3π/4)

(2, -5π/4)

(2, 11π/4)

(2, -3π/4)

(2, 5π/4)