Question

Find the rectangular coordinates of the point, whose cylindrical coordinates are given.

(a)(2, , e)
(b) (2, 3/2, 1 )

Answer 1

To find the rectangular coordinates of a point given in cylindrical coordinates, use the formulas x = r * cos(theta), y = r * sin(theta), and z = z. For cylindrical coordinates (2, 3/2, 1), the rectangular coordinates are (-√3, √3, 1).

Step-by-step explanation:

To find the rectangular coordinates of a point given in cylindrical coordinates, we can use the following formulas:

x = r * cos(theta)

y = r * sin(theta)

z = z

For part (a) with cylindrical coordinates (2, , e), since the theta value is missing, we cannot determine the rectangular coordinates with certainty. For part (b) with cylindrical coordinates (2, 3/2, 1), we can plug in the values into the formulas:

x = 2 * cos(3/2) = 2 * (-√3/2) = -√3

y = 2 * sin(3/2) = 2 * (√3/2) = √3

z = 1

Therefore, the rectangular coordinates are (-√3, √3, 1).