Table of contents

0. Review of College Algebra4h 43m
1. Measuring Angles40m
2. Trigonometric Functions on Right Triangles2h 5m
3. Unit Circle1h 19m
4. Graphing Trigonometric Functions1h 19m
5. Inverse Trigonometric Functions and Basic Trigonometric Equations1h 41m
6. Trigonometric Identities and More Equations2h 34m
7. Non-Right Triangles1h 38m
8. Vectors2h 25m
9. Polar Equations2h 5m
10. Parametric Equations1h 6m
11. Graphing Complex Numbers1h 7m

1. Measuring Angles

Angles in Standard Position

Trigonometry

1. Measuring Angles

Angles in Standard Position

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2:19 minutes

Problem 12

Textbook Question

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

Verified step by step guidance

Start by understanding that an angle in standard position has its vertex at the origin of the coordinate plane and its initial side along the positive x-axis.

Recognize that a negative angle is measured clockwise from the positive x-axis.

To draw -135°, begin at the positive x-axis and rotate clockwise.

Since -135° is more than -90° but less than -180°, the terminal side will be in the third quadrant.

Draw the terminal side of the angle such that it forms a 135° angle with the positive x-axis in the clockwise direction.

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Standard Position of an Angle

An angle is said to be in standard position when its vertex is at the origin of a coordinate system and its initial side lies along the positive x-axis. The angle is measured from the initial side to the terminal side, which is determined by the direction and magnitude of the angle. Positive angles are measured counterclockwise, while negative angles are measured clockwise.

Negative Angles

Negative angles are formed by rotating clockwise from the positive x-axis. For example, an angle of -135° indicates a rotation of 135° in the clockwise direction. Understanding how to visualize and draw negative angles is crucial for accurately representing them in standard position.

Quadrants of the Coordinate Plane

The coordinate plane is divided into four quadrants, each defined by the signs of the x and y coordinates. Quadrant I contains positive x and y values, Quadrant II has negative x and positive y values, Quadrant III has negative x and y values, and Quadrant IV has positive x and negative y values. Knowing which quadrant an angle lies in helps in determining the coordinates of points on the terminal side of the angle.