Question

In Exercises \(1-4,\) convert the point from cylindrical coordinates to rectangular coordinates. $$ (4, \pi / 2,-2) $$

Short answer

The rectangular coordinates of the given point in cylindrical coordinates are (0, 4, -2)

Step-by-step solution

Evaluate x

Substitute \(r = 4\) and \(\theta = \pi / 2\) into \(x = r \cos(\theta)\) to get \(x = 4 \cos(\pi / 2)\) which evaluates to \(x = 0\)

Evaluate y

Substitute \(r = 4\) and \(\theta = \pi / 2\) into \(y = r \sin(\theta)\) to get \(y = 4 \sin(\pi / 2)\) which evaluates to \(y = 4\)

Assign value of z

The z-coordinate is the same in both cylindrical and rectangular coordinate systems. So, \(z = -2\)