Chapter 14.5, Problem 1ST

To determine

To find: the rectangular coordinates in simplest radical form.

Answer to Problem 1ST

  $\left(2,-3.464\right)$ .

Explanation of Solution

Given:

The ninth root of unity.

Concept used:

The rectangular coordinate system consists of two real number lines that intersect at a right angle. The horizontal number line is called x-axis the point is called $\text{absicca}$ and vertical number line is called the y-axis and the point is called ordinate.

In first quadrant both the coordinates are positive.

In second quadrant x-coordinate is negative and y-coordinate is positive.

In third quadrant both coordinatesare negative.

In fourth quadrant x-coordinate is positive but y- coordinate is negative.

Calculation:

Coordinate given here is $\left(4,-{60}^0\right)$ .

In polar geometry the given two-point first point represent modulus of the equation second represent the argument of the equation.

  $\left(\text{r,θ}\right)$ .

  $\text{r=4}$ .

  ${\text{θ=-60}}^{\text{0}}$ .

  $\text{x=rcosθ, y=rsinθ}$ .

  $\text{x=4cos}\left({\text{-60}}^0\right)=2$ .

  $\text{y=4sin}\left(-{60}^0\right)=-3.464$ .

Hence, rectangular coordinates are: $\left(2,-3.464\right)$ .