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

0. Review of College Algebra

Basics of Graphing

Trigonometry

0. Review of College Algebra

Basics of Graphing

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2:31 minutes

Problem 8

Textbook Question

CONCEPT PREVIEW Fill in the blank(s) to correctly complete each sentence.The circle with equation x² + y² = 49has center with coordinates __ and radius equal to _.

Verified step by step guidance

Identify the standard form of a circle's equation, which is $ (x - h)^2 + (y - k)^2 = r^2 $, where $(h, k)$ is the center and $r$ is the radius.

Compare the given equation $ x^2 + y^2 = 49 $ with the standard form.

Notice that the equation can be rewritten as $ (x - 0)^2 + (y - 0)^2 = 49 $, indicating that $h = 0$ and $k = 0$.

Determine the center of the circle from the values of $h$ and $k$, which are both 0, so the center is $(0, 0)$.

Find the radius by taking the square root of 49, which is $r = \sqrt{49}$.

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Key Concepts

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

Circle Equation

The standard equation of a circle in a Cartesian coordinate system is given by (x - h)² + (y - k)² = r², where (h, k) is the center of the circle and r is the radius. In this case, the equation x² + y² = 49 can be rewritten to identify the center and radius directly.

Center of a Circle

The center of a circle is the point from which all points on the circle are equidistant. For the equation x² + y² = 49, the center is at the origin (0, 0) because there are no h or k values subtracted from x or y, indicating that the circle is centered at the coordinate axes.

Radius of a Circle

The radius of a circle is the distance from the center to any point on the circle. In the equation x² + y² = 49, the radius can be found by taking the square root of 49, which equals 7. Thus, the radius is 7 units.