Draw the polar oordinate `(3,(5pi)/(4))` on the plane.

Answer

To draw the polar coordinate \((3, \frac{5\pi}{4})\) on the plane, follow these steps:

### Step 1: Draw the Cartesian Coordinate System
- Begin by drawing the x-axis and y-axis, intersecting at the origin (0,0). This will form the Cartesian coordinate system.

### Step 2: Identify the Angle
- The angle given is \(\frac{5\pi}{4}\). This angle is measured in radians from the positive x-axis in a counter-clockwise direction.
- To visualize this, note that \(\frac{5\pi}{4}\) radians is equivalent to \(225^\circ\). This angle lies in the third quadrant of the coordinate system.

### Step 3: Locate the Angle on the Plane
- Starting from the positive x-axis, measure \(\frac{5\pi}{4}\) radians (or \(225^\circ\)). This will point towards the third quadrant.

### Step 4: Determine the Radius
- The radius given is \(3\). From the origin, measure a distance of \(3\) units along the direction of the angle \(\frac{5\pi}{4}\).

### Step 5: Mark the Point
- Mark the point that is \(3\) units away from the origin in the direction of the angle \(\frac{5\pi}{4}\). This point represents the polar coordinate \((3, \frac{5\pi}{4})\).

### Step 6: Label the Point
- Optionally, you can label the point as \(A(3, \frac{5\pi}{4})\) for clarity.

### Summary
You have successfully plotted the polar coordinate \((3, \frac{5\pi}{4})\) on the Cartesian plane.

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