Table of contents

0. Review of College Algebra4h 43m
1. Measuring Angles39m
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

1:30 minutes

Problem 1a

Textbook Question

In Exercises 1–6, the measure of an angle is given. Classify the angle as acute, right, obtuse, or straight. 135°

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Key Concepts

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

Types of Angles

Angles can be classified into four main types based on their measures: acute angles (less than 90°), right angles (exactly 90°), obtuse angles (greater than 90° but less than 180°), and straight angles (exactly 180°). Understanding these classifications is essential for determining the nature of any given angle.

Angle Measurement

Angles are measured in degrees, with a full rotation around a point equating to 360°. The measurement of an angle helps in identifying its classification. For example, an angle measuring 135° is greater than 90° but less than 180°, indicating it is obtuse.

Visual Representation of Angles

Visualizing angles can aid in their classification. Drawing angles on a coordinate plane or using protractors can help students see the differences between acute, right, obtuse, and straight angles. This visual understanding reinforces the theoretical definitions and classifications.