To draw the projections of a curve onto three coordinate planes, first draw the curve in three dimensions. Then, for each component of the vector equation of the curve, treat it as a parametric equation and graph it on the appropriate coordinate plane.
To identify the projections of the vector function, each component need to be treated as a parametric equation. The equation can be graphed on the XY coordinate plane and solved n terms of x and y.
We can use the trigonometry of a right triangle to figure out the equation for an ellipse in standard form. The x value in the formula comes from what is inside the sine function.
To graph a three-dimensional curve, you need to translate the projections of the curve into a three-dimensional coordinate system. Finding the initial value of the parameter at 0 can help you find a starting point for your graph.
The projection of a three dimensional curve onto two dimensional planes can be visualized by imagining the curve as a shadow cast by the plane. The projection in each plane is a curve that follows the shape of the plane.
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This video tutorial works through math problems/equations that address topics in Calculus 3, Vectors. This specific tutorial addresses Projections of the curve.
Length: 17 minutes
Copyright date: ©2013
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