It’s rare that Trigonometry is taught as its own course in Illinois. The material is most often part of Algebra 2 or Pre-Calculus courses. However, I have taught students who take Trigonometry as a separate course, and so I give it a separate category here.

Trigonometry is one of the first exposures to the mathematical structure of axioms, propositions, postulates, theorems and proofs. It’s also one of the first courses that will push a student to make real mathematical connections on his or her own, rather than just learning patterns of solving particular types of problems and repeating them.

Trigonometry begins with theorems about congruent triangles, specifically that right triangles with one angle known other than the right angle will have constant ratios of side lengths. These are used with basic geometry including the Pythagorean Theorem to define a handful of trigonometric relations, and a transition is made from the right-triangle definition of trigonometric ratios to the unit-circle definition.

From here, it’s possible to start studying how trigonometric functions interact with each other, and develop and prove (or disprove) conjectures on the same.

While the uses of Trigonometry may seem specialized, it will come up again in Calculus and is used frequently in basic physics, and is an essential component of a complete mathematical education.

I provide supplementary instruction (tutoring) for Trigonometry for $35 an hour. I provide more comprehensive homeschool instruction, including assigning homework and administering tests and quizzes for $50 an hour.