Lesson Plan: Tangents and Normals to the Graph of a Function Mathematics
This lesson plan includes the objectives, prerequisites, and exclusions of the lesson teaching students how to find the equations of tangents and normals to trigonometric, parametric, and implicitly defined curves using derivatives.
Students will be able to
- find tangents and normals to trigonometric and reciprocal trigonometric curves,
- find tangents and normals to parametric curves,
- find tangents and normals to curves using implicit differentiation,
- prove that two curves intersect orthogonally,
- solve word problems using tangents and normals to curves.
Students should already be familiar with
- differentiating polynomial, trigonometric, and reciprocal trigonometric functions,
- the chain, product, and quotient rules for differentiation,
- parametric differentiation,
- implicit differentiation.
Students will not cover
- equations with exponential or logarithmic terms.