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

1:12 minutes

Problem 5a

Textbook Question

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

Verified step by step guidance

Understand the classification of angles: acute (0 to π/2 radians), right (π/2 radians), obtuse (π/2 to π radians), and straight (π radians).

Identify the given angle measure, which is π radians.

Compare the given angle measure to the classifications: π radians is exactly equal to the measure of a straight angle.

Conclude that the angle is classified as a straight angle.

Remember that a straight angle forms a straight line and measures 180 degrees or π radians.

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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.

Radian Measure

In trigonometry, angles can be measured in degrees or radians. One complete revolution (360°) is equivalent to 2π radians. Therefore, π radians corresponds to 180°, which is classified as a straight angle. Familiarity with converting between these two units is crucial for angle classification.

Angle Classification Criteria

To classify an angle, one must compare its measure to the standard angle thresholds: less than 90° for acute, exactly 90° for right, between 90° and 180° for obtuse, and exactly 180° for straight. This systematic approach allows for accurate identification of the angle type based on its measure.