How to plot space curves with your TI

Andy Long

1. Use mode and set graphing to function, then set three function (e.g. y1, y2, and y3) to the components of r(t), the vector function. For example,

   

   of example #12, p. 876.

2. Choose two vectors to form a plane passing through the origin onto which you will project your space curve: that is, we will plot

    

   where I went with the two vectors and in class.

   These two orthogonal vectors form a new coordinate system whose normal vector can be taken to be (this is sometimes called the eye vector: it is as if we are staring at the origin down the vector ).

   The coordinates (1) above are given with respect to the vectors and .

3. We need to form the dot project, so we'll define variables constants a-f to hold the components of the u vectors:

   and .

   That is, use the STO button to store these values to the variables:

   

   

4. Switch your graphing mode to parametric, and define two functions to handle the coordinates of your projections of the three-dimensional space curve onto the new coordinate system represented by the two vectors above:

   

   

5. Staying in parametric graphing mode, set your window to an appropriate size (t domain, x domain, y domain), and graph.

Note: We've had trouble with trigonometric functions, when measured in degrees rather than radians. Be careful!

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