Trigonometry

This course is a part of Mathematics III, a 11-course Topic series from Khan Academy.

Learn about the definition of the basic trigonometric functions (sin(x), cos(x), and tan(x)), and use advanced trigonometric functions for various purposes.

This course contains 14 segments:

Law of sines

Learn about the Law of sines and how to use it in order to find missing side lengths and angles in general triangles.

Law of cosines

Learn about the Law of cosines and how to use it in order to find missing side lengths and angles in general triangles.

Solving general triangles

Use the power of trigonometry in order to solve various problems that involve triangles.

Introduction to radians

Learn about radians, which are the official unit of measurement for angles in algebra (in contrast to degrees, which are used in geometry).

Unit circle definition of sine, cosine, & tangent

Learn how the trigonometric ratios are extended to all real numbers using algebra. Start solving simple problems that involve this new definition of the trigonometric functions.

Graphs of sine, cosine, & tangent

Learn how the graphs of y=sin(θ), y=cos(θ), and y=tan(θ) look, using the unit circle definition of the functions.

Basic trigonometric identities

Learn about very useful trigonometric identities that arise by considering different properties of the unit circle definition.

Trigonometric values of special angles

Learn how to find the trigonometric values of some special angles without the use of a calculator.

Pythagorean identity

Prove the Pythagorean trigonometric identity for all real numbers and use it in order to solve problems.

Introduction to amplitude, midline, & extrema of sinusoidal functions

Learn about very important features of sinusoidal functions: the amplitude and the midline. Learn how they relate to the extremum points of the function.

Finding amplitude & midline from formula

Learn how to find the amplitude and the midline of the graph of a sinusoidal function from its formula. For example, find the amplitude and the midline of f(x)=3*sin(2x-1)+5.

Period of sinusoidal functions

Learn about the period of sinusoidal functions: how it relates to extremum points and the midline, and how to find it from the formula of the function. For example, find the period of f(x)=3*sin(2x-1)+5.

Graphing sinusoidal functions

Learn how to draw the graph of sinusoidal functions. For example, draw the graph of f(x)=-2*cos(πx)-7.

Constructing sinusoidal functions

Learn how to find the formula of a sinusoidal function from its graph or a few selected features. Model real-world situations with sinusoidal functions.