Precalculus

Take the function f(x) = 2sin(x) + 1 and ask what its graph looks like, where it repeats, and what happens when you stretch or shift it — answering that question well is roughly what Precalculus trains a student to do across every family of functions it covers: polynomial, rational, exponential, logarithmic, and trigonometric.

The course functions as a bridge, built specifically to prepare a student for the algebraic and graphical fluency Calculus assumes rather than teaches. Trigonometry usually takes up a large share of it: the unit circle, radian measure, graphing sine and cosine with amplitude and period changes, and trig identities that get used constantly in Calculus without being re-derived.

A common misread of Precalculus is treating it as a review course — extra practice on algebra already covered in Algebra II. It isn't. The material is genuinely new: function composition and inverses, piecewise functions, polar coordinates and vectors in some courses, and limits introduced informally as a preview of Calculus's central idea.

Students who arrive assuming it's a repeat often get caught off guard by how quickly it moves and how much it expects them to combine ideas from Algebra II (exponentials, logs, polynomial behavior) with material that's brand new. A tutor working on Precalculus tends to spend real time on the unit circle specifically, since so much of the trigonometry that follows depends on being able to recall it quickly rather than re-deriving sine and cosine values from scratch every time.