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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1:49 minutes

Problem 6

Textbook Question

In Exercises 1–6, the measure of an angle is given. Classify the angle as acute, right, obtuse, or straight.𝜋/2

Verified step by step guidance

Identify the given angle measure: \( \frac{\pi}{2} \).

Recall the classification of angles based on their measures in radians: acute (0 to \( \frac{\pi}{2} \)), right (\( \frac{\pi}{2} \)), obtuse (\( \frac{\pi}{2} \) to \( \pi \)), and straight (\( \pi \)).

Compare the given angle \( \frac{\pi}{2} \) with the standard angle measures.

Determine that \( \frac{\pi}{2} \) is exactly equal to the measure of a right angle.

Classify the angle as a right angle.

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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 identifying the nature of any given angle.

Radian Measure

Radian is a unit of angular measure used in mathematics. One complete revolution around a circle is 2π radians, which corresponds to 360 degrees. Therefore, π/2 radians is equivalent to 90 degrees, which is classified as a right angle.

Angle Classification Criteria

To classify an angle, one must compare its measure to the standard angle measures. An angle is classified as acute if it is less than 90°, right if it is exactly 90°, obtuse if it is between 90° and 180°, and straight if it is exactly 180°. This systematic approach allows for accurate identification of angles.