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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Problem 4

Textbook Question

CONCEPT PREVIEW Find the radius of each circle.

Verified step by step guidance

Step 1: Identify the given information about the circle, such as the diameter, circumference, or area.

Step 2: Recall the formulas related to the circle's radius: \( r = \frac{d}{2} \) for diameter \( d \), \( r = \frac{C}{2\pi} \) for circumference \( C \), and \( r = \sqrt{\frac{A}{\pi}} \) for area \( A \).

Step 3: Choose the appropriate formula based on the given information.

Step 4: Substitute the given values into the chosen formula.

Step 5: Solve the equation to find the radius of the circle.

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Key Concepts

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

Circle Definition

A circle is a set of points in a plane that are equidistant from a fixed point called the center. The distance from the center to any point on the circle is known as the radius. Understanding this definition is crucial for solving problems related to circles, including finding the radius when given other parameters.

Radius and Diameter Relationship

The radius of a circle is half the length of the diameter, which is the distance across the circle through its center. This relationship can be expressed mathematically as diameter = 2 × radius. Knowing this relationship allows for easy conversion between the two measurements when solving for the radius.

Circumference and Area Formulas

The circumference of a circle is the distance around it, calculated using the formula C = 2πr, where r is the radius. The area of a circle is given by A = πr². These formulas are essential for finding the radius when the circumference or area is provided, as they can be rearranged to solve for r.