**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 reductionâ€”reducing the given angle to a "reduced angle" inside a small range of angles? ¶

**A: **Yes, and say 0 to Ď€/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.