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Specifically, they are the inverses of the sine, cosine, tangent, cotangent, secant, and cosecant functions, [4] and are used to obtain an angle from any of the angle's trigonometric ratios. Inverse trigonometric functions are widely used in engineering , navigation , physics , and geometry .
2.3 Differentiating the inverse tangent function. 2.4 Differentiating the inverse cotangent function. 2.5 Differentiating the inverse secant function.
A formula for computing the trigonometric identities for the one-third angle exists, but it requires finding the zeroes of the cubic equation 4x 3 − 3x + d = 0, where is the value of the cosine function at the one-third angle and d is the known value of the cosine function at the full angle.
2.5 Proof of compositions of trig and inverse trig functions. 3 See also. 4 Notes. 5 References. Toggle the table of contents. Proofs of trigonometric identities. 5 ...
for the definition of the principal values of the inverse hyperbolic tangent and cotangent. In these formulas, the argument of the logarithm is real if and only if z is real. For artanh, this argument is in the real interval (−∞, 0] , if z belongs either to (−∞, −1] or to [1, ∞) .
The Taylor series for the inverse tangent function, often called Gregory's series, is = + + = = + +. The Leibniz formula is the special case arctan 1 = 1 4 π . {\textstyle \arctan 1={\tfrac {1}{4}}\pi .} [ 3 ]
Inverse secant; Inverse sine; Inverse tangent; Inverse vercosine; Inverse versine This page was last edited on 5 March 2020, at 10:32 (UTC). Text ...
In calculus, the inverse function rule is a formula that expresses the derivative of the inverse of a bijective and differentiable function f in terms of the derivative of f. More precisely, if the inverse of f {\displaystyle f} is denoted as f − 1 {\displaystyle f^{-1}} , where f − 1 ( y ) = x {\displaystyle f^{-1}(y)=x} if and only if f ...