Circling the Tangent is a lesson for students in a high school level calculus course or precalculus class.
TSW learn and write the equations for circles.
TSW solve equations to find values from inputs.
TSW define tangent and normal lines.
TSW use definitions of tangents and normals with the circle equation to create a unique artwork.
Instructions.
Students will wite 5 equations. Each for a circle with a radius of 8 units. The centers are the origin and then in each quadrant such that four circles are tangent to both the x and y axises.
Students then use the equation for the circle centered at (8,8) to identify and plot the cooresponding values for when x=0,1,2,4,6,8,10,12,14,15,16.
Next they label the points for the other ones (students may choose to do the center circle after the first 4 are done.
Once the points are plotted, students use a drawing triangle with the right angle on the plotted points and one side going through the center as a radius (or normal).
The other leg of the triangle will be at right angles to the normal and be a tangent. Draw that line to the edge of the quadrant that circle is is.
After one of these is done for each point on a circle, the student will come back and use a straight edge to extend the tangent lines in the other direction.
Students then do the same for the centered circle.
Upon satisfactory completion, creators then color the drawing as they wish.