How do you change (23, 2, −1) from rectangular to cylindrical coordinates?

Step 1 First, you have to calculate the radius r=x2+y2=12+4=4 Second, you know that x=rcos⁡(θ) and y=rsin⁡(θ), therefore, cos⁡(θ)=32 and y=12 So, θ=π6 (modulo 2π) Conclusion, the cylindrical coordinates are (4, π6, −1)

Resolved: "How do you change (23, 2, −1) from..."

High School
Calculus and Analysis
Calculus 2
Parametric equations

Jackson David

Answered question

2022-02-02

How do you change

(2 \sqrt{3}, 2, - 1)

from rectangular to cylindrical coordinates?

Answer & Explanation

dimljenihhml

Beginner2022-02-03Added 15 answers

Step 1
First, you have to calculate the radius

r = \sqrt{x^{2} + y^{2}} = \sqrt{12 + 4} = 4

Second, you know that

x = r \cos (θ)

and

y = r \sin (θ)

,
therefore,

\cos (θ) = \frac{\sqrt{3}}{2}

and

y = \frac{1}{2}

So,

θ = \frac{π}{6}

(modulo

2 π

)
Conclusion, the cylindrical coordinates are

(4, \frac{π}{6}, - 1)

Do you have a similar question?

Recalculate according to your conditions!

New Questions in Calculus 2

What is the derivative of the work function?
How to use implicit differentiation to find $\frac{d y}{d x}$ given $3 x^{2} + 3 y^{2} = 2$ ?
How to differentiate $y = \log x^{2}$ ?
The solution of a differential equation y′′+3y′+2y=0 is of the form
A) $c_{1} e^{x} + c_{2} e^{2 x}$
B) $c_{1} e^{- x} + c_{2} e^{3 x}$
C) $c_{1} e^{- x} + c_{2} e^{- 2 x}$
D) $c_{1} e^{- 2 x} + c_{2} 2^{- x}$
How to find instantaneous velocity from a position vs. time graph?
How to implicitly differentiate $\sqrt{x y} = x - 2 y$ ?
What is 2xy differentiated implicitly?
How to find the sum of the infinite geometric series given $1 + \frac{2}{3} + \frac{4}{9} + ...$ ?
Look at this series: 1.5, 2.3, 3.1, 3.9, ... What number should come next?
A. 4.2
B. 4.4
C. 4.7
D. 5.1
What is the derivative of $\frac{x + 1}{y}$ ?
How to find the sum of the infinite geometric series 0.9 + 0.09 + 0.009 +…?
How to find the volume of a cone using an integral?
What is the surface area of the solid created by revolving $f (x) = e^{2 - x}, x \in [1, 2]$ around the x axis?
How to differentiate $x^{\frac{2}{3}} + y^{\frac{2}{3}} = 4$ ?
The differential coefficient of $\sec (\tan^{- 1} (x))$ .

Didn't find what you were looking for?