Trigonometry

Trigonometry is the study of angles and triangles. It began as a way to find distances that are hard to measure, such as the height of a mountain or the distance to a ship. Today it also describes anything that repeats in cycles, such as sound waves, tides, and alternating current.

These lessons cover a first college course in trigonometry. They prepare you for calculus and physics. You should know the algebra in our College Algebra course, especially functions, graphs, and inverse functions. Start with Chapter 1.

Angles and the trigonometric functions

Degrees and radians, arc length and angular speed; the six trigonometric functions of right triangles and of any angle; the unit circle; and solving right triangles.

Graphs of the trigonometric functions

Graphs of sine and cosine; amplitude, period, and phase shift; graphs of tangent, cotangent, secant, and cosecant; and modeling with sine waves.

Trigonometric identities

The fundamental identities and how to prove an identity; sum and difference formulas; double-angle and half-angle formulas; and product-to-sum formulas.

Inverse functions and trigonometric equations

The inverse sine, cosine, and tangent functions; and solving trigonometric equations, including ones that need identities.

Triangles and vectors

The law of sines and the law of cosines; the area of a triangle; vectors in the plane; and the dot product.

Polar coordinates and complex numbers

Polar coordinates and graphs of polar equations; the trigonometric form of a complex number; and De Moivre’s theorem and roots of complex numbers.

Conic sections and parametric equations

Parabolas, ellipses, and hyperbolas; rotation of axes; polar equations of conics; and parametric equations.