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.