Question

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

Explanation:

Step1: Understand polar coordinates

Polar coordinates are given as \((r,\theta)\), where \(r = 4\) (the distance from the origin) and \(\theta=-\frac{\pi}{4}\) (the angle measured from the positive \(x -\)axis in the clockwise direction).

Step2: Locate the angle

Starting from the positive \(x -\)axis, rotate clockwise by an angle of \(\frac{\pi}{4}\).

Step3: Locate the radius

Since each circular grid line is \(0.5\) units apart, and \(r = 4\), move \(4\div0.5=8\) grid - line intervals from the origin along the ray corresponding to the angle \(\theta =-\frac{\pi}{4}\).

Answer:

Plot a point \(8\) grid - line intervals (since \(r = 4\) and each grid line is \(0.5\) units) from the origin along the ray that is at an angle of \(-\frac{\pi}{4}\) (clockwise from the positive \(x -\)axis).