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Ch. 5 - Complex Numbers, Polar Coordinates and Parametric Equations
Blitzer - Trigonometry 3rd Edition
Blitzer3rd EditionTrigonometryISBN: 9780137316601Non è quello che usi tu?Cambia libro di testo
Tutti i libri di testoBlitzer 3rd EditionCh. 5 - Complex Numbers, Polar Coordinates and Parametric EquationsProblema 2
Capitolo 5, Problema 2

In Exercises 1–8, parametric equations and a value for the parameter t are given. Find the coordinates of the point on the plane curve described by the parametric equations corresponding to the given value of t. x = 7 − 4t, y = 5 + 6t; t = 1

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Identify the given parametric equations: \(x = 7 - 4t\) and \(y = 5 + 6t\), and the given parameter value \(t = 1\).
Substitute the value of \(t = 1\) into the equation for \(x\): calculate \(x = 7 - 4 \times 1\).
Substitute the value of \(t = 1\) into the equation for \(y\): calculate \(y = 5 + 6 \times 1\).
Simplify both expressions to find the numerical values of \(x\) and \(y\) at \(t = 1\).
Write the coordinates of the point on the curve as \((x, y)\) using the values found in the previous step.

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Parametric Equations

Parametric equations express the coordinates of points on a curve as functions of a parameter, usually denoted as t. Instead of y as a function of x, both x and y depend on t, allowing the description of more complex curves and motions.
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Parameterizing Equations

Substitution of Parameter Values

To find a specific point on a parametric curve, substitute the given parameter value into the parametric equations. This yields the corresponding x and y coordinates, pinpointing the exact location on the curve for that parameter.
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Eliminating the Parameter

Coordinate Plane and Points

The coordinate plane is a two-dimensional space defined by x (horizontal) and y (vertical) axes. Points are represented as ordered pairs (x, y), which locate positions on the plane. Understanding this helps interpret the results of parametric equations.
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Determining Different Coordinates for the Same Point
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