This topic is a quick review for readers who need a reminder about this area of mathematics. If you’re familiar with trigonometry, you can skip this topic. If you find this topic difficult to follow, you might consult a more basic reference on mathematics.

Trigonometric functions are principally used to model or describe:

• The relation between angles in a triangle (hence the name).
• Rotations about a circle, including locations given in polar coordinates.
• Cyclical or periodic values, such as sound waves.

The three basic trigonometric functions are derived from an angle rotating about a unit circle.

The tangent function is undefined for x=0. Another way to define the tangent is:

Because XYR defines a right-angled triangle, the relation between the sine and cosine is:

The graphs of the basic trigonometric functions illustrate their cyclical nature.

The sine and cosine functions yield the same values, but the phase differs along the X axis by /2: in other words, 90 degrees.

The inverse functions for the trigonometric functions are the arc functions; the inverse only applies to values of x restricted by –/2 ≤ X ≤ /2. The graphs for these functions appear like the basic trigonometric function graphs, but turned on their sides.

The hyperbolic functions are based on the exponential constant e instead of on circular measurement. However, they behave similarly to the trigonometric functions and are named for them. The basic hyperbolic functions are: