Please forward this error screen to 31. Please forward this error screen to 101. For the similarity csc it, see Cosine similarity.

Basis of trigonometry: if two right triangles have equal acute angles, they are similar, so their side lengths are proportional. The most familiar trigonometric functions are the sine, cosine, and tangent. More precise definitions are detailed below. Trigonometric functions are commonly defined as ratios of two sides of a right triangle containing the angle, and can equivalently be defined as the lengths of various line segments from a unit circle. In this use, trigonometric functions are used, for instance, in navigation, engineering, and physics. In modern usage, there are six basic trigonometric functions, tabulated here with equations that relate them to one another. Especially with the last four, these relations are often taken as the definitions of those functions, but one can define them equally well geometrically, or by other means, and then derive these relations.

Angles A and B may vary. Bottom: Graph of sine function versus angle. Angles from the top panel are identified. Plot of the six trigonometric functions and the unit circle for an angle of 0. The notion that there should be some standard correspondence between the lengths of the sides of a triangle and the angles of the triangle comes as soon as one recognizes that similar triangles maintain the same ratios between their sides. To define the trigonometric functions for the angle A, start with any right triangle that contains the angle A. The hypotenuse is always the longest side of a right-angled triangle.