Chapter 8.1, Problem 19E

To determine

To calculate : To determine which point in the below figure P, Q, R or S has the polar coordinates

  

Answer to Problem 19E

The point in the figure that has the given Polar Coordinates $r=4,\theta =-23\pi /4$ is $P\left(4,-23\pi /4\right)$ .

Explanation of Solution

Given: Polar coordinate is $\left(4,-23\pi /4\right)$

Formula Used:

A polar equation is any equation that describes a relation between r and θ, where r represents the distance from the pole (origin) to a point on a curve, and θ represents the counter-clockwise angle made by a point on a curve, the pole, and the positive x-axis.

Calculation:

  $\theta =-23\pi /4$ can be written as:

  $\theta =-\left(6\pi -\frac{\pi }{4}\right)$

Plotting the values in the polar coordinates using the above definition as reference, point $S$ satisfies the conditions.

Hence, the point in the figure that has the given Polar Coordinates $r=4,\theta =-23\pi /4$ is $P\left(4,-23\pi /4\right)$ .

Conclusion:

The point in the figure that has the given Polar Coordinates $r=4,\theta =-23\pi /4$ is $P\left(4,-23\pi /4\right)$ .