convert the point from polar to cartesian coordinates. write your answer in the simplest form or rounded to…

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 = 1) and (\theta=\frac{5\pi}{6}).

Step2: Calculate the (x) - coordinate

We know that (\cos\frac{5\pi}{6}=-\frac{\sqrt{3}}{2}). Substitute (r = 1) and (\theta=\frac{5\pi}{6}) into (x=r\cos\theta). (x = 1\times\cos\frac{5\pi}{6}=-\frac{\sqrt{3}}{2}\approx - 0.87)

Step3: Calculate the (y) - coordinate

We know that (\sin\frac{5\pi}{6}=\frac{1}{2}). Substitute (r = 1) and (\theta=\frac{5\pi}{6}) into (y = r\sin\theta). (y=1\times\sin\frac{5\pi}{6}=\frac{1}{2}=0.5)

Answer:

The Cartesian coordinates are (\left(-\frac{\sqrt{3}}{2},\frac{1}{2}\right)) or approximately ((-0.87,0.5))