Represents the initial angle of the object when thrown, and h Projectile motion depends on two parametric equations:.Equations that are not functions can be graphed and used in many applications involving motion. Parametric equations allow the direction or the orientation of the curve to be shown on the graph.When graphing a parametric curve by plotting points, note the associated t-values and show arrows on the graph indicating the orientation of the curve.To graph parametric equations by plotting points, make a table with three columns labeled.When there is a third variable, a third parameter on whichĭepend, parametric equations can be used.Graphing Parametric Equations on the TI-84.To the horizontal, with initial speed v 0 ,Īccess the following online resource for additional instruction and practice with graphs of parametric equations. The path of an object propelled at an inclination of θ To the horizontal, with an initial speed of v 0 , In this type of motion, an object is propelled forward in an upward direction forming an angle of θ Parametric equations, however, illustrate how the values of x and y change depending on t, as the location of a moving object at a particular time.Ī common application of parametric equations is solving problems involving projectile motion. Although rectangular equations in x and y give an overall picture of an object's path, they do not reveal the position of an object at a specific time. Many of the advantages of parametric equations become obvious when applied to solving real-world problems. The graph of the parametric equations is in red and the graph of the rectangular equation is drawn in blue dots on top of the parametric equations. The ellipse is mapped in a counterclockwise direction as shown by the arrows indicating increasing t We see that the parametric equations represent an ellipse. Using angles with known sine and cosine values for t As long as we are careful in calculating the values, point-plotting is highly dependable.Ĭonstruct a table like that in using angle measure in radians as inputs for t , In lieu of a graphing calculator or a computer graphing program, plotting points to represent the graph of an equation is the standard method. Graphing Parametric Equations by Plotting Points In this section, we’ll discuss parametric equations and some common applications, such as projectile motion problems. How far will the ball travel? Will it clear the fence for a game-winning home run? The outcome may depend partly on other factors (for example, the wind), but mathematicians can model the path of a projectile and predict approximately how far it will travel using parametric equations. The batter swings and hits the baseball at 140 feet per second and at an angle of approximately 45° It is the bottom of the ninth inning, with two outs and two men on base. Graph plane curves described by parametric equations by plotting points.
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