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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1:43 minutes

Problem 1

Textbook Question

CONCEPT PREVIEW Fill in the blank(s) to correctly complete each sentence.The point (-1, 3)lies in quadrant ________ in the rectangular coordinate system.

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Identify the coordinates of the point, which are (-1, 3).

Recall that the rectangular coordinate system is divided into four quadrants.

Understand that in the coordinate system, the x-axis is horizontal and the y-axis is vertical.

Recognize that the sign of the x-coordinate and y-coordinate determines the quadrant: Quadrant I (+,+), Quadrant II (-,+), Quadrant III (-,-), Quadrant IV (+,-).

Determine that since the x-coordinate is negative and the y-coordinate is positive, the point (-1, 3) lies in Quadrant II.

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Key Concepts

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

Quadrants in the Coordinate System

The rectangular coordinate system is divided into four quadrants based on the signs of the x and y coordinates. Quadrant I has positive x and y values, Quadrant II has negative x and positive y values, Quadrant III has negative x and y values, and Quadrant IV has positive x and negative y values. Understanding these quadrants is essential for determining the location of points in the plane.

Coordinate Points

A coordinate point is represented as an ordered pair (x, y), where 'x' indicates the horizontal position and 'y' indicates the vertical position on the coordinate plane. The first value corresponds to the x-coordinate, which determines the point's distance from the y-axis, while the second value corresponds to the y-coordinate, indicating its distance from the x-axis. This structure is fundamental for locating points in the coordinate system.

Sign of Coordinates

The sign of the coordinates (positive or negative) determines the quadrant in which a point lies. For example, a point with a negative x-coordinate and a positive y-coordinate, like (-1, 3), will be located in Quadrant II. Recognizing the significance of these signs is crucial for accurately identifying the position of points in the coordinate system.