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

Radians

Trigonometry

1. Measuring Angles

Radians

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1:38 minutes

Problem 21

Textbook Question

In Exercises 21–28, convert each angle in radians to degrees.𝜋2

Verified step by step guidance

Understand the relationship between radians and degrees: 180 degrees is equivalent to \( \pi \) radians.

To convert radians to degrees, use the formula: \( \text{Degrees} = \text{Radians} \times \frac{180}{\pi} \).

Identify the given angle in radians, which is \( \frac{\pi}{2} \).

Substitute \( \frac{\pi}{2} \) into the conversion formula: \( \text{Degrees} = \frac{\pi}{2} \times \frac{180}{\pi} \).

Simplify the expression by canceling out \( \pi \) and multiplying the remaining numbers to find the angle in degrees.

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Key Concepts

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

Radians and Degrees

Radians and degrees are two units for measuring angles. A full circle is 360 degrees, which is equivalent to 2π radians. To convert between these units, the relationship can be used: 180 degrees equals π radians. Understanding this relationship is essential for converting angles accurately.

Conversion Formula

The conversion from radians to degrees can be performed using the formula: degrees = radians × (180/π). This formula allows for straightforward calculations when converting any angle expressed in radians to its degree equivalent, ensuring clarity in angular measurements.

Understanding π

The constant π (pi) is approximately 3.14159 and represents the ratio of a circle's circumference to its diameter. In trigonometry, π is crucial for defining angles in radians. Recognizing how π relates to angles helps in visualizing and solving problems involving circular motion and periodic functions.