Question

Different Polar Coordinates for the Same Point Plot the point that has the given polar coordinates. Then give two other polar coordinate representations of the point, one with$r<0$ and the other with$r>0$$(3,\frac{\pi }{2})$

Short answer

The graph of a given point,

The other two points are,$(3,\frac{5\pi }{2})$$(-3,\frac{3\pi }{2})$

Step-by-step solution

Step 1. Given information

A point in polar coordinates as $(3,\frac{\pi }{2})$

Step 2. Concept used

Point is given in the polar coordinate system, plot, or represent on the graph. The first coordinate represents radius and the second coordinate represents angle.

Step 3. Calculation

The radius and angle are given as,$\begin{array}{l}r=3\\ \theta =\frac{\pi }{2}\end{array}$

Now plot the plot on the graph and we get,

Now for, add into the coordinate-

$\begin{array}{l}\Rightarrow (3,\frac{\pi }{2})=(3,\frac{\pi }{2}+2\pi )\\ \Rightarrow (3,\frac{\pi }{2})=(3,\frac{5\pi }{2})\end{array}$

For$r<o$, change the sign of radius and add to angle given-

$\begin{array}{l}\Rightarrow (3,\frac{\pi }{2})=\left((-3),\pi +\frac{\pi }{2}\right)\\ \Rightarrow (3,\frac{\pi }{2})=(-3,\frac{3\pi }{2})\end{array}$