derivative of sin

Let us learn about Derivative of sin

The derivative of a function at a point measures the rate at which the function's value changes as the function's argument changes. That is, a derivative provides a mathematical formulation of the notion of rate of change. As it turns out, the derivative is an extremely versatile concept which can be viewed in many different ways. For example, referring to the two-dimensional graph of f, the derivative can also be regarded as the slope of the tangent to the graph at the point x. The slope of this tangent can be approximated by a secant. Given this geometrical interpretation, it is not surprising that derivatives can be used to determine many geometrical properties of graphs of functions, such as concavity or convexity.

In mathematics, the trigonometric functions are functions of an angle. It is also called as circular function. They are used to relate the angles of a triangle to the lengths of the sides of a triangle. The most familiar trigonometric functions are the sine, cosine, and tangent. Six trigonometric functions are one-to-one; they must be restricted in order to have inverse function. Integrate the function f(x) with respect to x can be written as ⌠f(x) dx.

Except where otherwise noted, the trigonometric functions take a radian angle as input and the inverse trigonometric functions return radian angles.

The ordinary trigonometric functions are single-valued functions defined everywhere in the complex plane (except at the poles of tan, sec, csc, and cot). They are defined generally via the exponential function, e.g.

cos(x) = e^ix+e^-ix/2

The inverse trigonometric functions are multivalued, thus requiring branch cuts, and are generally real-valued only on a part of the real line. Definitions and branch cuts are given in the documentation of each function. The branch cut conventions used by mpmath are essentially the same as those found in most standard mathematical software, such as Mathematica and Python’s own cmath libary (as of Python 2.6; earlier Python versions implement some functions erroneously).

In our next blog we shall learn about "how many sides does a hexagon have"

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