Chapter 1, Problem 322RE

True or False? Justify your answer with a proof or a counter example.

322. The rectangular coordinates of the point $\left(4,\frac{5\pi }{6}\right)$ are $\left(2\sqrt{3},-2\right)$

To determine

To find:

Rectangular coordinates of the $(4,5\pi /6)$ are $\left(2\surd 3,-2\right)$.

Answer to Problem 322RE

The statement “Rectangular coordinates of the $(4,5\pi /6)$ are $\left(2\surd 3,-2\right)$ ” is False.

Explanation of Solution

Given:

Point is given as $(4,5\pi /6)$

$x=rcos\theta$ and $y=rsin\theta$

Here,

$r=4$ and $\theta =5\pi /6$

$cos\left(\frac{5\pi }{6}\right)=\frac{-\surd 3}{2}$

$sin\left(\frac{5\pi }{6}\right)=\frac{1}{2}$

$\begin{array}{l}\text{So, }\\ \left(x,y\right)=\left(-2\surd 3,2\right)\end{array}$

Therefore this statement is false.