![]() artanh(x) is the only solution to tanh(y) = x. artanh ( x ) ¶Ĭompute the area hyperbolic tangent of x, the inverse function to tanh(). The function only accepts dimensionless arguments. In complex mode, the function is defined for any complex z as arcosh(z) = ln. In real mode, the parameter x must be > 1. Except for x=1, the second solution to this equation will be given by -arcosh(x). arcosh(x) is the positive solution to cosh(y) = x. arcosh ( x ) ¶Ĭompute the area hyperbolic cosine of x, the inverse function to cosh(). In complex mode, the function is defined for any complex z as arsinh(z) = ln. arsinh(x) is the only solution to cosh(y) = x. arsinh ( x ) ¶Ĭompute the area hyperbolic sine of x, the inverse function to sinh(). In complex mode, any complex number may be used as the argument. Hyperbolic & Inverse Hyperbolic ¶ sinh ( x ) ¶ The argument values must be dimensionless. Unlike arctan() this function only accepts real arguments. When radians are set as the angle unit, the return value lies in the range ]-π, π]. In degrees mode, this function returns a value in the range ]-180, 180]. The behavior of the function depends on the angle unit setting (degrees or radians). However, the function handles vectors in other quadrants as well. both x > 0 and y > 0 are true), it is given by arctan(y/x). If the point (x, y) lies in the first quadrant (i.e. Returns the angle formed by the vector (x, y) and the X axis. The argument of arctan() must be dimensionless. When complex numbers are enabled in addition, arctan() may take any argument from the complex plane, except for +j and -j. When radians are set as the angle unit, arctan() maps a real number to a value in. Complex arguments are not allowed in degrees mode. In degrees mode, arctan() takes a real argument, and the return value is in the range. The behavior of the function depends on both the angle unit setting (degrees or radians) and on whether complex numbers are enabled. Returns the inverse tangent of x, such that tan(arctan(x)) = x. ![]() In complex mode, arcsin(-1) = π/2 and arcsin(1) = π/2 will yield the same result as in real mode. When complex numbers are enabled in addition, arcsin() may take any argument from the complex plane. When radians are set as the angle unit, arcsin() maps an element from to a value in. Real arguments outside and complex numbers are not allowed in degrees mode. ![]() In degrees mode, arcsin() takes a real argument from, and the return value is in the range. Returns the inverse sine of x, such that sin(arcsin(x)) = x. The argument of arccos() must be dimensionless. In complex mode, arccos(-1) = π and arccos(1) = 0 will yield the same result as in real mode. When complex numbers are enabled in addition, arccos() may take any argument from the complex plane. When radians are set as the angle unit, arccos() maps an element from to a value in. In degrees mode, arccos() takes a real argument from, and the return value is in the range. Returns the inverse cosine of x, such that cos(arccos(x)) = x. The argument of csc() must be dimensionless. When radians are set as the angle unit, csc() will be 2π-periodic. Complex arguments are not allowed in degrees mode, regardless of the corresponding setting. In degrees mode, the argument is assumed to be expressed in degrees, such that csc() is periodic with a period of 360 degrees: csc(x) = csc(x+360). The behavior depends on both the angle unit setting (degrees or radians) and on whether complex numbers are enabled. Returns the cosecant of x, defined as the reciprocal sine of x: csc(x) = 1/sin(x). The argument of sec() must be dimensionless. ![]() |x|>10 77, SpeedCrunch no longer recognizes the periodicity of the function and issues an error. The argument may be complex.įor real arguments beyond approx. When radians are set as the angle unit, sec() will be 2π-periodic. In degrees mode, the argument is assumed to be expressed in degrees, such that sec() is periodic with a period of 360 degrees: sec(x) = sec(x+360). ![]() Returns the secant of x, defined as the reciprocal cosine of x: sec(x) = 1/cos(x). ![]()
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