Question

How do you plot the point $(4,270\,\,\, degrees)$

Answer 1

Here in this question we have to plot the graph for the given points. Here we have the points in the polar form; we have converted it into Cartesian form. Hence by considering the points we plot the graph for the given question. hence the solution is obtained for the given question.

Complete step-by-step solution:
Here in this question, we have to plot the graph for the given function. A graph of a function is a set of ordered pairs and it is represented as $y = f(x)$, where x and f(x) are real numbers. These pairs are in the form of cartesian form and the graph is the two-dimensional graph.
Here the given point is in the form of polar form. The general polar form is represented as $(r,\theta )$
While converting the polar form into cartesian form $x = r\cos \theta$ and $y = r\sin \theta$. Here the value of r is 4 and $\theta$ is ${270^ \circ }$.
Therefore the value of x and y is determined by
$x = 4\cos \left( {{{270}^ \circ }} \right)$
The value of $\cos (270)$ is 0. Therefore the value of x is

$$\Rightarrow x = 4.(0) \\\ \Rightarrow x = 0 \\\$$

The value of y is
$y = 4\sin \left( {{{270}^ \circ }} \right)$
The value of $\sin (270)$ is -1. Therefore the value of x is

$$\Rightarrow y = 4.( - 1) \\\ \Rightarrow y = - 4 \\\$$

Here we have a point, usually the point is generally represented as $(x,y)$. The first term represents the x value and the second term represents the y value. Here we have to plot the graph for the point $(0, - 4)$. Here when the x value is 0, then the value of y is -4. The point will be on the y axis.
From the origin of a graph we have to move 4 steps downwards for the point (0, -4).
Therefore the graph for the points is plotted as shown below:

Note: The graph is plotted x-axis versus y axis. The graph is two dimensional. By the equation of a graph, we can plot the graph by assuming the value of x. We can’t assume the value of y. because the value of y depends on the value of x. Hence, we have plotted the graph.