2. 三角函数的定义 2. The definition of trigonometric functions

[ 三角函数的定义和符号变化 ] [Definitions and symbols change trigonometric]

名称 Name

正弦 Sine

余弦 Cosine

正切 Tangent

余切 Cotangent

正割 Secant

余割 Cosecant

定 Fixed

义 Righteousness

符 Symbol

号 Number

与 Versus

增 Increase

减 Less

变 Change

化 Of

Ⅰ Ⅰ

+ ↑ + ↑

+ ↓ + ↓

+ ↑ + ↑

+ ↓ + ↓

+ ↑ + ↑

+ ↓ + ↓

Ⅱ Ⅱ

+ ↓ + ↓

- ↓ - ↓

- ↑ - ↑

- ↓ - ↓

- ↑ - ↑

+ ↑ + ↑

Ⅲ Ⅲ

- ↓ - ↓

- ↑ - ↑

+ ↑ + ↑

+ ↓ + ↓

- ↓ - ↓

- ↑ - ↑

Ⅳ Ⅳ

- ↑ - ↑

+ ↑ + ↑

- ↑ - ↑

- ↓ - ↓

+ ↓ + ↓

- ↓ - ↓

[ 三角函数的图形与特征 ] [Graphics and features trigonometric functions]

标准正弦曲线 Standard sinusoidal

周期: Cycle:

与 x 轴交点(同拐点): Intersection with the x-axis (with the inflection point):

极值点(极大点或极小点): Extreme point (maximum point or minimum point):

余弦曲线 Cosine curve

周期: Cycle:

与 x 轴交点(同拐点): Intersection with the x-axis (with the inflection point):

极值点: Extreme point:

   一般正弦曲线 General sinusoidal

                        周期: Cycle:

式中 A >0 为振幅, Where A> 0 is an amplitude, 为角频率, Is the angular frequency, 为初相 For the initial phase           与 x 轴交点(同拐点): Intersection with the x-axis (with the inflection point):

         

             极值点: Extreme point:

         

                                                

   同时, At the same time, 也属于一般正弦曲线 ( 设 Also belong to the general sine curve (set ,可化为 , Can be turned into ) )

它是将标准正弦曲线在 y 轴方向上伸 It is a standard sine curve extending in the y-axis direction          长 A 倍,在 x 轴方向上压缩 A long times, compressed in the x-axis direction 倍,并 向左平移 Times, and pan left 一段距离而得到 . And get some distance.

正切曲线 Tangent curve

               周期: Cycle:

               与 x 轴交点(同拐点): Intersection with the x-axis (with the inflection point):

       , ,

            该点切线斜率为 1. The slope of a tangent point.

               渐近线: Asymptote:

余切曲线 Cotangent curve

  

                  周期: Cycle:

                  与 x 轴交点(同拐点): Intersection with the x-axis (with the inflection point):

              , ,

                  该点切线斜率为- 1. The slope of the tangent point - 1.

                  渐近线: Asymptote:

正割曲线 Secant curve

               周 Week   期: Period:

               极大点: Great point:

               极小点: Minimum points:

               渐近线: Asymptote:

余割曲线 Cosecant curve

                周 Week   期: Period:

                极大点: Great point:

                极小点: Minimum points:

                        

                渐近线: Asymptote: