Trigonometry

This course is a part of Geometry (all content), a 17-course Topic series from Khan Academy.

Triangles are not always right (although they are never wrong), but when they are it opens up an exciting world of possibilities. Not only are right triangles cool in their own right (pun intended), they are the basis of very important ideas in analytic geometry (the distance between two points in space) and trigonometry.

This course contains 11 segments:

Special right triangles

We hate to pick favorites, but there really are certain right triangles that are more special than others. In this tutorial, we pick them out, show why they're special, and prove it! These include 30-60-90 and 45-45-90 triangles (the numbers refer to the measure of the angles in the triangle).

Introduction to the trigonometric ratios

Learn what sine, cosine, and tangent are.

Solving for a side in a right triangle using the trigonometric ratios

Learn how to find a side length in a right triangle when given one side length and one acute angle.

Solving for an angle in a right triangle using the trigonometric ratios

Learn how to find an acute angle in a right triangle when given two side lengths.

Modeling with right triangles

Solve real-world problems that can be modeled by right triangles, using trigonometry.

Trigonometric ratios and similarity

Learn how the trigonometric ratios are derived from triangle similarity considerations.

Sine and cosine of complementary angles

Learn about the relationship between the sine of an angle and the cosine of its complementary angle, which is the angle that completes to 90°.

The reciprocal trigonometric ratios

Learn about the remaining three side ratios in a right triangle: the secant, the cosecant, and the cotangent.

The 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.

The 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.