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 |
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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: