Question

plot the point given by the following polar coordinates on the graph below. each circular grid line is 0.5 units apart. $\left(-1,\frac{3\pi}{4}\
ight)$

Explanation:

Step1: Understand polar coordinates

Polar coordinates are given as \((r,\theta)\). Here \(r=- 1\) and \(\theta=\frac{3\pi}{4}\). When \(r<0\), we find the angle \(\theta+\pi\) and use \(|r|\). So \(\theta+\pi=\frac{3\pi}{4}+\pi=\frac{3\pi + 4\pi}{4}=\frac{7\pi}{4}\) and \(|r| = 1\).

Step2: Locate the angle

On the polar graph, find the angle \(\frac{7\pi}{4}\). The angle \(\frac{7\pi}{4}\) is in the fourth - quadrant.

Step3: Locate the radius

Since each circular grid line is \(0.5\) units apart and \(|r| = 1\), move \(1\) unit (which is \(2\) grid - lines of \(0.5\) units each) from the origin along the ray corresponding to the angle \(\frac{7\pi}{4}\).

Answer:

Plot the point \(1\) unit from the origin along the ray \(\theta=\frac{7\pi}{4}\) (equivalent to the polar coordinates \((-1,\frac{3\pi}{4})\)).