91Ó°ÊÓ

Imagine the Cartesian Coordinate System as a big cross on a piece of graph paper. It's made up of two main lines: the horizontal line called the x-axis, and the vertical line called the y-axis. These axes meet at a point right in the middle, the origin, which is labeled as (0,0).
This system is super useful because it helps us locate points in space using coordinates. Every point on this plane can be described as a pair of numbers ig( x, y ig), where **x** is how far along you are on the x-axis, and **y** is how far along you are on the y-axis.
The **x-axis** runs horizontally across, and values increase to the right and decrease to the left. For the **y-axis**, imagine it going up and down, with values increasing upwards and decreasing downwards.

The Cartesian plane is split into four sections, called quadrants, by the x and y-axes. Think of these as the four corners of a square.

• **Quadrant I** is at the top right. Here, both x and y values are positive.
• **Quadrant II** lies at the top left, with negative x values and positive y values.
• **Quadrant III** is at the bottom left, where both x and y coordinates are negative.
• Finally, **Quadrant IV** is at the bottom right, having positive x values but negative y values.

When plotting an angle in standard position, its initial side is always on the positive x-axis. Each quadrant can tell us important information about where this angle ends up, which is vital when sketching angles like -270 degrees.

Angles can be measured in either direction from the positive x-axis. Positive angles turn counterclockwise, but what if an angle is negative?
A **negative angle** means you switch directions and measure clockwise from the positive x-axis.
For example, let's talk about the angle -270°. Starting from the positive x-axis, you move clockwise around the quadrants. With -270°, you make a full circle and land back on the positive y-axis, residing in quadrant I with its terminal side along the negative y-axis.

When measuring angles, deciding the direction is key. **Clockwise measurement** is used for negative angles.
Picture a clock: the hands move from 12 to 3 in the same direction as we measure negative angles.
Start from the positive x-axis and follow around the circle. For instance, with -270°, imagine turning a complete circle plus a quarter turn in clockwise rotation, which takes you to the positive y-axis.

• First 90° brings you to the negative y-axis in quadrant III.
• An additional 180° (270° total) positions you on the positive y-axis.

This method helps accurately determine where angles lie on the Cartesian plane.