![]() The notations sin −1( x), cos −1( x), tan −1( x), etc. In computer programming languages, the inverse trigonometric functions are often called by the abbreviated forms asin, acos, atan. Depending upon your instructor, you may be expected to memorize these antiderivatives. Below we make a list of derivatives for these functions. All these functions are continuous and differentiable in their domains. Thus in the unit circle, "the arc whose cosine is x" is the same as "the angle whose cosine is x", because the length of the arc of the circle in radii is the same as the measurement of the angle in radians. \displaystyle\int\cos x\,dx\sin x+C In the video, we work out the antiderivatives of the four remaining trig functions. The basic trigonometric functions include the following 6 functions: sine (sin x), cosine (cos x), tangent (tan x), cotangent (cot x), secant (sec x), and cosecant (csc x). When measuring in radians, an angle of θ radians will correspond to an arc whose length is rθ, where r is the radius of the circle. (This convention is used throughout this article.) This notation arises from the following geometric relationships: The most common convention is to name inverse trigonometric functions using an arc- prefix: arcsin( x), arccos( x), arctan( x), etc. Several notations for the inverse trigonometric functions exist. See also: Trigonometric functions § Notation ![]()
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