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

Previous problemNext problem

1:29 minutes

Problem 27

Textbook Question

Concept Check Graph the points on a coordinate system and identify the quadrant or axis for each point.(4.5, 7)

Verified step by step guidance

Step 1: Understand the coordinate system, which consists of the x-axis (horizontal) and y-axis (vertical).

Step 2: Identify the coordinates given, which are (4.5, 7). Here, 4.5 is the x-coordinate and 7 is the y-coordinate.

Step 3: Plot the point (4.5, 7) on the coordinate plane. Start at the origin (0,0), move 4.5 units to the right along the x-axis, and then move 7 units up parallel to the y-axis.

Step 4: Determine the quadrant where the point is located. Since both x and y coordinates are positive, the point (4.5, 7) is in the first quadrant.

Step 5: Review the characteristics of the first quadrant, where both x and y values are positive, confirming the location of the point.

Verified video answer for a similar problem:

This video solution was recommended by our tutors as helpful for the problem above

Video duration:

Play a video:

Was this helpful?

Key Concepts

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

Coordinate System

A coordinate system is a two-dimensional plane defined by a horizontal axis (x-axis) and a vertical axis (y-axis). Each point on this plane is represented by an ordered pair (x, y), where 'x' indicates the horizontal position and 'y' indicates the vertical position. Understanding this system is crucial for locating points accurately.

Quadrants

The coordinate plane is divided into four quadrants, each representing a different combination of positive and negative values for x and y. Quadrant I contains points where both coordinates are positive, Quadrant II has a negative x and positive y, Quadrant III has both negative coordinates, and Quadrant IV has a positive x and negative y. Identifying the correct quadrant is essential for graphing points.

Axes

The axes in a coordinate system are the two perpendicular lines that define the plane: the x-axis (horizontal) and the y-axis (vertical). Points that lie directly on an axis have one coordinate equal to zero. Understanding the role of axes helps in determining the location of points relative to the origin (0,0) and in identifying whether a point lies on an axis or in a quadrant.