# Trigonometric Functions FAQs:

Q: Are trigonometric functions important in the study of triangles and modeling periodic phenomena?

A: Yes, and among many other applications.

Q: Are trigonometric functions periodic?

A: Yes, and hence not injective, so strictly they do not have an inverse function.

Q: Are trigonometric functions defined on the complex numbers using the Taylor series above?

A: Yes.

Q: Are trigonometric functions the sine?

A: Yes, and cosine, and tangent.

Q: Are trigonometric functions analytic functions?

A: Yes.

Q: Are trigonometric functions commonly taught in the order sine?

A: Yes, and cosine, tangent.

Q: Are trigonometric functions used?

A: Yes, for instance, in navigation, engineering, and physics.

Q: Is a trigonometric function range reduction—reducing the given angle to a "reduced angle" inside a small range of angles?

A: Yes, and say 0 to π/2, using the periodicity and symmetries of the trigonometric functions.

Q: Are trigonometric functions also important in physics?

A: Yes.

Q: Are trigonometric functions commonly defined as ratios of two sides of a right triangle containing the angle?

A: Yes, and can equivalently be defined as the lengths of various line segments from a unit circle.

Q: Are trigonometric functions a complicated subject?

A: Yes, and which can today be avoided by most people because of the widespread availability of computers and scientific calculators that provide built-in trigonometric functions for any angle.

Q: Are trigonometric functions summarized in the following table and described in more detail below?

A: Yes.

Q: Is a trigonometric function bijective?

A: Yes.