Question

polar coordinates of a point are given. find the rectangular coordinates of the point.
(6,180°)
the rectangular coordinates of the point are
(type an ordered pair. simplify your answer, including any radicals. use integers or fractions for any numbers in the expression.)

Explanation:

Step1: Identify polar coordinates

Given polar coordinates $(r, \theta) = (6, 180^\circ)$

Step2: Calculate x-coordinate

Use $x = r\cos\theta$. $\cos180^\circ = -1$, so $x = 6\times(-1) = -6$

Step3: Calculate y-coordinate

Use $y = r\sin\theta$. $\sin180^\circ = 0$, so $y = 6\times0 = 0$

Answer:

$(-6, 0)$