Mathematics · High School (11–12)

A taxi fare depends on the distance. The height of a ball depends on the time. A temperature in kelvin depends on a temperature in celsius. In each case, one number decides another, and mathematics has one word for this: a function. In this chapter we start from sets and relations, and we build the idea of a function with care. Then we draw functions, move and stretch their graphs, combine them, and undo them with the inverse. Python draws the graphs and checks our answers.

A Ferris wheel turns, a tide rises and falls, a guitar string shakes. Each motion repeats itself, and the trigonometric functions describe all of them. In this chapter you measure angles in radians, extend sine, cosine and tangent to angles of any size with the unit circle, draw their graphs, and prove the formulas for the sum and the difference of two angles. Python draws the graphs and checks each identity at thousands of angles.