In Exercises 8–12, draw each angle in standard position. -135°

Verified step by step guidance

1. Understand that an angle in standard position has its vertex at the origin and its initial side along the positive x-axis.
2. Since the angle given is -135°, recognize that the negative sign indicates a clockwise rotation from the positive x-axis.
3. Measure 135° clockwise starting from the positive x-axis to locate the terminal side of the angle.
4. Note that rotating 135° clockwise is equivalent to rotating 225° counterclockwise (since 360° - 135° = 225°), so the terminal side lies in the third quadrant.
5. Draw the angle by first drawing the initial side along the positive x-axis, then rotating clockwise 135° to draw the terminal side, which will point diagonally in the third quadrant.

Key Concepts

Standard Position of an Angle

An angle is in standard position when its vertex is at the origin of the coordinate plane, and its initial side lies along the positive x-axis. The angle is measured by rotating the initial side to the terminal side, either counterclockwise for positive angles or clockwise for negative angles.

Measuring Negative Angles

Negative angles are measured by rotating the initial side clockwise from the positive x-axis. For example, a -135° angle means rotating 135 degrees clockwise, which places the terminal side in the third quadrant of the coordinate plane.

Quadrants and Angle Placement

The coordinate plane is divided into four quadrants, each corresponding to a range of angles. Understanding which quadrant an angle's terminal side lies in helps in accurately drawing and interpreting the angle in standard position.