Question

How to plot whose polar coordinates are given $\left( {2,\dfrac{{ - 17}}{5}\pi } \right)$?

Answer 1

Hint: In this question we have to plot the point on the graph, to do this first locate the angle on the polar coordinate plane, then determine where the radius intersects the angle, then plot the point, we will get the required point on the graph.

Complete step by step answer:
Polar coordinate form in terms of$\left( {r,\theta } \right)$, where $r$ is the distance of the point from the origin and$\theta $is the angle between the lines joining origin and the point and positive axis.
In polar coordinates, a point in the plane is determined by its distance $r$ from the origin and the angle$\theta $ (in radians) between the line from the origin to the point and the x-axis. The polar coordinate system is a two-dimensional coordinate system in which each point on a plane is determined by a distance from a reference point and an angle from a reference direction In polar coordinates the origin is often called the pole.
Given polar coordinates are $\left( {2,\dfrac{{ - 17}}{5}\pi } \right)$,
So, here radical coordinate $r = 2$ and,
Angular coordinate $\theta = \dfrac{{ - 17}}{5}\pi $,
First on a Polar graph, draw an angle of $\dfrac{{ - 17}}{5}\pi $with respect to $x$-axis and by taking radius 2,
And the point at which the line intersects the radius that is $r = 2$will be our polar coordinate.
The required point on the graph is,

Note: Polar coordinates are based on angles, unlike Cartesian coordinates, polar coordinates have many different ordered pairs. Because infinitely many values of theta have the same angle in standard position, an infinite number of coordinate pairs describe the same point. Also, a positive and a negative coterminal angle can describe the same point for the same radius, and because the radius can be either positive or negative, you can express the point with polar coordinates in many ways.