Chapter 9.1, Problem 66AYU

In Problems 57-68, the rectangular coordinates of a point are given. Find polar coordinates for each point.

$\left(-2.3,0.2\right)$

To determine

To find: Find polar coordinates for the given rectangular coordinates.

Answer to Problem 66AYU

$(2.31,-{4.97}^{\circ })$

Explanation of Solution

Given:

$r\text{cos}\theta =-2.3, r\text{sin}\theta =0.2\to p\left(x,y\right)=\left(-2.3,0.2\right)$

Calculation:

$r=\sqrt{x^2+y^2}$ and $\theta ={\text{tan}}^{-1}(\frac{y}{x})$

To find $r$ we know that $r=\sqrt{x^2+y^2}$.

So $r=\sqrt{{\left(-2.3\right)}^2+{\left(0.2\right)}^2}=\sqrt{5.29+0.04}\approx 2.31$

And $\text{tan}\theta = \frac{y}{x}\to \theta ={\text{ tan}}^{-1}(\frac{y}{x})$

$\theta ={\text{ tan}}^{-1}(\frac{0.2}{-2.3})={\text{ tan}}^{-1}(-0.09) \approx -{4.97}^{\circ }$

Hence, polar system coordinates are $(2.31,-{4.97}^{\circ })$.