The y-coordinate is the vertical position of a point on a coordinate plane, measured as the distance from the x-axis. It represents the up-down position of a point and is used to describe the location of objects or data points within a two-dimensional coordinate system.
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The y-coordinate is the vertical component of a point's location on a coordinate plane, measured from the x-axis.
In the Cartesian coordinate system, the y-coordinate is the second value in an ordered pair (x, y) that describes a point's position.
The y-coordinate is essential for graphing functions, as it determines the vertical position of a point on the graph.
In the unit circle, the y-coordinate of a point on the circle corresponds to the sine value of the angle formed by the point and the positive x-axis.
Parametric equations use a parameter, often denoted as 't', to define the x and y coordinates of a point as functions of that parameter.
Review Questions
Explain the role of the y-coordinate in the Cartesian coordinate system and how it is used to describe the location of points.
In the Cartesian coordinate system, the y-coordinate represents the vertical position of a point on the coordinate plane, measured as the distance from the x-axis. The y-coordinate, along with the x-coordinate, forms an ordered pair (x, y) that uniquely identifies the location of a point. The y-coordinate is essential for graphing functions, as it determines the vertical position of a point on the graph. For example, the point (3, 5) has an x-coordinate of 3 and a y-coordinate of 5, indicating that it is located 5 units above the x-axis and 3 units to the right of the origin.
Describe the relationship between the y-coordinate and the trigonometric function sine in the context of the unit circle.
In the unit circle, the y-coordinate of a point on the circle corresponds to the sine value of the angle formed by the point and the positive x-axis. The unit circle is a circle with a radius of 1 unit, centered at the origin (0, 0) of a coordinate plane. As a point moves around the unit circle, its y-coordinate changes, and this change is directly related to the sine function. Specifically, the y-coordinate of a point on the unit circle is equal to the sine of the angle formed by the point and the positive x-axis. This relationship between the y-coordinate and the sine function is fundamental to understanding trigonometric functions and their applications.
Analyze the role of the y-coordinate in the context of parametric equations and how it is used to describe the graph of a curve.
Parametric equations use a parameter, often denoted as 't', to define the x and y coordinates of a point as functions of that parameter. In this context, the y-coordinate is one of the two equations that together describe the position of a point on a curve. The y-coordinate equation, along with the x-coordinate equation, allows the parametric equations to define the shape and location of a curve on a coordinate plane. By varying the parameter 't', the y-coordinate changes, which, in combination with the changing x-coordinate, traces out the shape of the curve. This flexibility in defining the x and y coordinates separately through parametric equations enables the representation of a wide range of curves that may not be easily expressed using a single equation in terms of x and y.
A two-dimensional coordinate system where the position of a point is determined by its horizontal (x-coordinate) and vertical (y-coordinate) distances from the origin.