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Graphs of sine, cosine and tangent The sine function (blue) ... This is the smallest period, except for the tangent and the cotangent, which have ...
The trigonometric functions are periodic with common period ... Tangent = [6 ...
The tangent line to a point on a differentiable curve can also be thought of as a tangent line approximation, the graph of the affine function that best approximates the original function at the given point. [3] Similarly, the tangent plane to a surface at a given point is the plane that "just touches" the
Abu al-Wafa had sine tables in 0.25° increments, to 8 decimal places of accuracy, and accurate tables of tangent values. [16] He also made important innovations in spherical trigonometry [17] [18] [19] The Persian polymath Nasir al-Din al-Tusi has been described as the creator of trigonometry as a mathematical discipline in its own right.
Cotangent begins its period at , finishes it at +, and then repeats it (forward) over + to +. This periodicity is reflected in the general inverses, where k {\displaystyle k} is some integer. The following table shows how inverse trigonometric functions may be used to solve equalities involving the six standard trigonometric functions.
Graph of the tangent-function tan(x). One period from -½π to ½π is drawn. x- and y-axis have the same units. One period from -½π to ½π is drawn. x- and y-axis have the same units. All labels are embedded in "Computer Modern" font.
The constant function f (x) = c, where c is independent of x, is periodic with any period, but lacks a fundamental period. A definition is given for some of the following functions, though each function may have many equivalent definitions.
The sides of this rhombus have length 1. The angle between the horizontal line and the shown diagonal is 1 / 2 (a + b).This is a geometric way to prove the particular tangent half-angle formula that says tan 1 / 2 (a + b) = (sin a + sin b) / (cos a + cos b).