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

Fixed

Righteousness

Symbol

Number

Versus

Increase

Less

Change

Of

+ +

+ +

+ +

+ +

+ +

+ +

+ +

- -

- -

- -

- -

+ +

- -

- -

+ +

+ +

- -

- -

- -

+ +

- -

- -

+ +

- -

[ 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:

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:

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           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 ( 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          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:

               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:

                  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

               Week   期: Period:

               极大点: Great point:

               极小点: Minimum points:

               渐近线: Asymptote:

余割曲线 Cosecant curve

                Week   期: Period:

                极大点: Great point:

                极小点: Minimum points:

                        

                渐近线: Asymptote: