Ch stands for hyperbolic cosine function, which is generally recorded as cosh or abbreviated as ch.
Hyperbolic sine function and hyperbolic cosine function are two basic hyperbolic functions, from which hyperbolic tangent function can be derived.
The definition of hyperbolic sine function is: sinh=(e? -e)/2. When the absolute value of x is large, the graph of hyperbolic sine function approaches the curve y=e in the first quadrant. /2, the curve near the third quadrant y=-e/2. When x=0, sinhx=sinh0=0.
Hyperbolic cosine function's definition is: cosh=(e? +e)/2. When x=0, cosh0= 1 is the minimum value of this function.
Extended data
The relationship between hyperbolic function and trigonometric function
Augustus de morgan extended circular trigonometry to hyperbola in the textbook Trigonometry and Bioalgebra published in 1849, and William Kinton Clifford parameterized the unit hyperbola with hyperbolic angle in 1878.
Given the same angle α, the hyperbolic angle (hyperbolic sector area divided by radius) is calculated on hyperbola to get hyperbolic function, and the angle α gets trigonometric function. On the unit circle and unit hyperbola, hyperbolic function and trigonometric function have the following relationship:
(1) Sine is also the half chord from the X axis to the curve.
(2) Cosine is also the half chord from the Y axis to the curve (Cosine is the other side of the rectangle in the figure).
(3) The tangent line is also the length of the tangent line on the curve from a point on the X axis (1, 0) to the end edge.
(4) The cotangent is also the length of the intersection of the tangent from the Y axis and the ending edge and the curve, and the intersection of the Y axis and the curve.
(5) Secant is also on a right triangle with tangent and unit length, but the sides are different.
(6) Cotangent is also the distance between the intersection point and origin of the tangent line of the Y axis and the intersection point of the curve and the end point of the Y axis.
Baidu encyclopedia-hyperbolic sine function
Baidu Encyclopedia-hyperbolic cosine function
Baidu encyclopedia-hyperbolic function