convert the following point from polar to cartesian coordinates. write the exact answer as an ordered pair…

Explanation:

Step1: Recall the conversion formulas

For a polar point ((r,\theta)), the Cartesian coordinates ((x,y)) are given by (x = r\cos\theta) and (y=r\sin\theta). Here (r = 3) and (\theta=-\frac{11\pi}{6}).

Step2: Find the (x) - coordinate

Use the formula (x = r\cos\theta). Since (\cos(-\frac{11\pi}{6})=\cos(\frac{11\pi}{6})) (because (\cos(-\alpha)=\cos\alpha)), and (\cos(\frac{11\pi}{6})=\cos(2\pi-\frac{\pi}{6})=\cos\frac{\pi}{6}=\frac{\sqrt{3}}{2}). So (x = 3\times\frac{\sqrt{3}}{2}=\frac{3\sqrt{3}}{2}).

Step3: Find the (y) - coordinate

Use the formula (y = r\sin\theta). Since (\sin(-\frac{11\pi}{6})=-\sin(\frac{11\pi}{6})) (because (\sin(-\alpha)=-\sin\alpha)), and (\sin(\frac{11\pi}{6})=\sin(2\pi - \frac{\pi}{6})=-\sin\frac{\pi}{6}=-\frac{1}{2}). So (y=3\times(- (-\frac{1}{2}))=\frac{3}{2}).

Answer:

((\frac{3\sqrt{3}}{2},\frac{3}{2}))