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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
1.3 Notation. 1.4 Alternative ... 1.6.2 Using the Taylor series and Newton's method for the inverse function. ... to convert it to the standard normal distribution.
Functions included square root, inverse, trigonometric (sine, cosine, tangent and their inverses), exponentiation, logarithms and factorial. The HP-65 was one of the first calculators to include a base conversion function, although it only supported octal (base 8) conversion.
A ray through the unit hyperbola x 2 − y 2 = 1 at the point (cosh a, sinh a), where a is twice the area between the ray, the hyperbola, and the x-axis. For points on the hyperbola below the x -axis, the area is considered negative (see animated version with comparison with the trigonometric (circular) functions).
A complex number can be visually represented as a pair of numbers (a, b) forming a vector on a diagram called an Argand diagram, representing the complex plane. Re is the real axis, Im is the imaginary axis, and i is the "imaginary unit", that satisfies i 2 = −1.
According to the Pythagorean theorem, for a right triangle with side lengths and , the length of the hypotenuse can be calculated as +. This formula defines the Pythagorean addition operation, denoted here as : for any two real numbers and , the result of this operation is defined to be [3] = +.
A method analogous to piece-wise linear approximation but using only arithmetic instead of algebraic equations, uses the multiplication tables in reverse: the square root of a number between 1 and 100 is between 1 and 10, so if we know 25 is a perfect square (5 × 5), and 36 is a perfect square (6 × 6), then the square root of a number greater than or equal to 25 but less than 36, begins with ...