3. 反双曲函数的定义、图形与特征 3. Definition of inverse hyperbolic functions, graphics and features
[ 反双曲函数的定义及其对数表达式 ] [Definition inverse hyperbolic function and its logarithmic expression]
函 Letter 数 Number | 记 Remember 号 Number | 对数表达式 Logarithmic expression |
反双曲正弦 Inverse hyperbolic sine | 若 x = sh y , If x = sh y, 则 y = Ar sh x Then y = Ar sh x |  |
反双曲余弦 Inverse hyperbolic cosine | 若 x = If x = ch y , ch y, 则 y = Ar ch x Then y = Ar ch x |  |
反双曲正切 Inverse hyperbolic tangent | 若 x = th y , If x = th y, 则 y = Ar th x Then y = Ar th x |  |
反双曲余切 Inverse hyperbolic cotangent | 若 x = cth y , If x = cth y, 则 y = Ar cth x Then y = Ar cth x |  |
反双曲正割 Inverse Hyperbolic Secant | 若 x = sech y , If x = sech y, 则 y = Ar sech x Then y = Ar sech x |  |
反双曲余割 Inverse hyperbolic cosecant | 若 x = csch x , If x = csch x, 则 y = Ar csch x Then y = Ar csch x |  |
[ 反双曲函数的图形与特征 ] [Graphics and features inverse hyperbolic function]
反双曲正弦曲线反双曲余弦曲线 Inverse hyperbolic sine curve inverse hyperbolic cosine curve
曲线关于原点对称 . 曲线关于x轴对称 . Curve symmetric about the origin of the curve on the x-axis symmetry.
拐点 （ 同曲线对称中心 ）： Inflection (with the curve center of symmetry): 顶点 ： Vertex: 
， 该点切线斜率为 1 The slope of a tangent point
反双曲正切曲线 Inverse hyperbolic tangent curve 反双曲余切曲线 Inverse hyperbolic cotangent curve
曲线关于原点对称 . 曲线关于原点对称 . Curve symmetrical about the origin curve symmetrical about the origin.
拐点 （ 同曲线对称中心 ）： 不连续点 ： Inflection (curve with the center of symmetry): discontinuity: 
， 该点切线斜率为 1 渐近线 ： The slope of a tangent point asymptote: 
反双曲正割曲线反双曲余割曲线 Inverse hyperbolic secant hyperbolic cosecant curve curve
曲线关于x轴对称 . 曲线关于原点对称 . Curve on the x-axis symmetry. Curve symmetric about the origin.
顶点 ： Vertex: 
不连续点 ： Discontinuous points: 
拐点 ： Inflection point: 
渐近线 ： Asymptote: 
和 And 