What is the Cartesian form of $(3, \frac{- 5 π}{2})$ $( 3, (-5pi)/2 )$ ?

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Answer 1 · 2018-02-14T08:36:02

Using the formulas:
$x = r \cdot cos (θ)$ $x=r*cos(theta)$
$y = r \cdot sin (θ)$ $y=r*sin(theta)$

our answer is $(0, - 3)$ $(0,-3)$ in Cartesian

To convert from Polar coordinates to Cartesian, we must apply the following formulas:

$x = r \cdot cos (θ)$ $x=r*cos(theta)$
$y = r \cdot sin (θ)$ $y=r*sin(theta)$

where polar form is $(r, θ)$ $(r,theta)$
and Cartesian form is $(x, y)$ $(x,y)$

for x:
$x = 3 \cdot cos (- 5 \frac{π}{2}) = 3 \cdot 0 = 0$ $x=3*cos(-5pi/2) = 3*0 = 0$

$y = 3 \cdot sin (- 5 \frac{π}{2}) = 3 \cdot - 1 = - 3$ $y=3*sin(-5pi/2) = 3*-1 = -3$

thus converting from polar to Cartesian:

Cartesian = $(0, - 3)$ $(0,-3)$

What is the Cartesian form of (3,−5π2)( 3, (-5pi)/2 ) ?