Questions: Express the point given in Cartesian coordinates in cylindrical coordinates (r, θ, z).
A) (9(1/2), 9(sqrt(3)/2),-6)=()
()
()
B) (-9(1/2), 9(sqrt(3)/2),-6)=()
()
()
C) (9(1/2),-9(sqrt(3)/2),-6)=()
()
()
D) (-9(1/2),-9(sqrt(3)/2),-6)=()
()
()
Transcript text: (1 point) Express the point given in Cartesian coordinates in cylindrical coordinates $(r, \theta, z)$.
A) $\left(9\left(\frac{1}{2}\right), 9\left(\frac{\sqrt{3}}{2}\right),-6\right)=($ $\square$
$\square$
$\square$ )
B) $\left(-9\left(\frac{1}{2}\right), 9\left(\frac{\sqrt{3}}{2}\right),-6\right)=($ $\square$
$\square$
$\square$ )
C) $\left(9\left(\frac{1}{2}\right),-9\left(\frac{\sqrt{3}}{2}\right),-6\right)=($ $\square$
$\square$
$\square$ )
D) $\left(-9\left(\frac{1}{2}\right),-9\left(\frac{\sqrt{3}}{2}\right),-6\right)=($ $\square$
$\square$
$\square$ )
Solution
Solution Steps
To convert Cartesian coordinates (x,y,z) to cylindrical coordinates (r,θ,z), we use the following formulas:
r=x2+y2
θ=atan2(y,x)
The z-coordinate remains the same.
We will apply these formulas to each of the given points.
Step 1: Convert Point A
For point A, given the Cartesian coordinates (9(21),9(23),−6):