We have an answer to "What is the Cartesian form of (12,5π3)?"

Fastage6bk

Answered question

2022-02-03

What is the Cartesian form of

(12, \frac{5 π}{3})

Answer & Explanation

Nathan Huang

Beginner2022-02-04Added 15 answers

Explanation:
Remember that polar coordinates are of the form

(r, θ)

.
Also, remember that our x-values correspond with cosine and y-values with sine.
Then, remember that our sine and cosine values come from the unit circle, where

r = 1

. So, when changing our coordinates from polar to cartesian coordinates we are taking

(r, θ) \to (r \cos (θ), r \sin (θ))

.
Notice that

\frac{5 π}{3} = 2 π - \frac{π}{3}

. So, we can say that

θ = - \frac{π}{3}

, which is in the fourth quadrant. This means that cosine is positive, and sine is negative.
Then we can essentially say that

(12, \frac{5 π}{3}) \to (12 \cos (\frac{π}{3}), - 12 \sin (\frac{π}{3})) = (12 (\frac{1}{2}), - 12 (\frac{\sqrt{3}}{2})) = (6, - 6 \sqrt{3})

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 $\sec (\tan^{- 1} (x))$ .