Graphs of the trigonometric functions

The trigonometric functions repeat their values over and over. Their graphs are waves. This chapter draws these graphs and shows how to stretch and shift them. It ends by using sine waves to describe things that repeat, such as a bouncing spring, the tides, and the hours of daylight.

From this chapter on, angles and numbers are in radians unless a degree sign is shown.

This chapter covers the following topics:

Graphs of sine and cosine

The graphs of ${y=\sin x}$ and ${y=\cos x}$, their key points, and their properties: domain, range, period, zeros, and symmetry.

Amplitude, period, and phase shift

Stretching and shifting sine and cosine graphs, graphing ${y=a\sin k(x-b)+d}$, and finding an equation from a graph.

Graphs of tangent, cotangent, secant, and cosecant

The graphs of the other four trigonometric functions, their vertical asymptotes and periods, and their transformations.

Modeling with sinusoids

Simple harmonic motion, frequency, modeling repeating data such as daylight hours and tides, and damped motion.

Practice questions

Practice problems on every section of this chapter, with full step-by-step solutions.