6. -/1 points details my notes larpcalclimaga7 9.5.028. use a graphing utility to find the rectangular…

Explanation:

Step1: Recall conversion formulas

The conversion from polar coordinates $(r,\theta)$ to rectangular coordinates $(x,y)$ is given by $x = r\cos\theta$ and $y=r\sin\theta$. Here $r = 5$ and $\theta=\frac{11\pi}{9}$.

Step2: Calculate the x - coordinate

$x = 5\cos(\frac{11\pi}{9})$. Using a calculator, $\cos(\frac{11\pi}{9})\approx - 0.766$, so $x=5\times(-0.766)=-3.83$.

Step3: Calculate the y - coordinate

$y = 5\sin(\frac{11\pi}{9})$. Using a calculator, $\sin(\frac{11\pi}{9})\approx - 0.643$, so $y = 5\times(-0.643)=-3.215\approx - 3.22$.

Answer:

$(-3.83,-3.22)$