学习目标：

利用matplotlib 和 numpy 画三角函数曲线

学习内容：

正弦，余弦，正切，余切函数曲线
双曲正弦，双曲余弦，双曲正切，双曲余切函数曲线
反正弦，反余弦，反正切，反余切函数曲线
反双曲正弦，反双曲余弦，反双曲正切，反双曲余切函数曲线

学习产出：

1.1， python画正弦函数曲线，保持原有的position不变的情况，代码如下：

import numpy as np
from matplotlib import pyplot as plt plt.figure(figsize = (6, 8), dpi = 200) # create a frame, dpi = 200
plt.subplot(111)    #create a subgraph, grid = 1 * 1x = np.linspace(-np.pi, np.pi, 256, endpoint = True)  #numpy array:[-π, π], total 256 values
y = np.sin(x)plt.plot(x, y, color = 'blue', linewidth = 2.0, linestyle= '-')      #define line color and styleplt.xlim(x.min() * 1.1, x.max() * 1.1)     #limit x range
plt.ylim(y.min() * 1.1, y.max() * 1.1)     #limit y rangeplt.xticks([-np.pi,-np.pi/2,0,np.pi/2,np.pi],[r'$-\pi$',r'$-\pi/2$',r'$0$',r'$\pi/2$',r'$\pi$'])   # 5 values in x_axis
plt.yticks([-1,-0.5,0,0.5,1],[r'$-1$',r'$-0.5$',r'$0$',r'$0.5$',r'$1$'])   # 5 values in y-axisplt.show()

正弦曲线图片如下：

利用spine，在数据区域的边界，可以放置在任意位置, 在上述代码中加入，完整的代码和曲线如下：

import numpy as np
from matplotlib import pyplot as plt plt.figure(figsize = (6, 8), dpi = 200) # create a frame, dpi = 200
plt.subplot(111)    #create a subgraph, grid = 1 * 1x = np.linspace(-np.pi, np.pi, 256, endpoint = True)  #numpy array:[-π, π], total 256 values
y = np.sin(x)plt.plot(x, y, color = 'blue', linewidth = 2.0, linestyle= '-')      #define line color and styleplt.xlim(x.min() * 1.1, x.max() * 1.1)     #limit x range
plt.ylim(y.min() * 1.1, y.max() * 1.1)     #limit y rangeplt.xticks([-np.pi,-np.pi/2,0,np.pi/2,np.pi],[r'$-\pi$',r'$-\pi/2$',r'$0$',r'$\pi/2$',r'$\pi$'])   # 5 values in x_axis
plt.yticks([-1,-0.5,0,0.5,1],[r'$-1$',r'$-0.5$',r'$0$',r'$0.5$',r'$1$'])   # 5 values in y-axis#move the boundary line,set origin is 0
ax = plt.gca()  #get current line position
ax.xaxis.set_ticks_position('bottom')
ax.yaxis.set_ticks_position('left')
ax.spines['bottom'].set_position(('data', 0))  #set bottom position to 0
ax.spines['left'].set_position(('data', 0))
ax.spines['top'].set_color('none')      #cancel original boundary
ax.spines['right'].set_color('none')plt.show()

去掉边框的正弦曲线图片如下：

1.2， python画余弦函数曲线，我们在正弦曲线的代码中加入z = np.cos(x)的代码，同时需要区分正弦曲线和余弦曲线：

import numpy as np
from matplotlib import pyplot as plt plt.figure(figsize = (6, 8), dpi = 200) # create a frame, dpi = 200
plt.subplot(111)    #create a subgraph, grid = 1 * 1x = np.linspace(-np.pi, np.pi, 256, endpoint = True)  #numpy array:[-π, π], total 256 values
y = np.sin(x)
z = np.cos(x)plt.plot(x, y, color = 'blue', linewidth = 2.0, linestyle= '-')      #define line color and style
plt.plot(x, z, color = 'red', linewidth = 2.0, linestyle= '-')plt.xlim(x.min() * 1.1, x.max() * 1.1)     #limit x range
plt.ylim(y.min() * 1.1, y.max() * 1.1)     #limit y rangeplt.xticks([-np.pi,-np.pi/2,0,np.pi/2,np.pi],[r'$-\pi$',r'$-\pi/2$',r'$0$',r'$\pi/2$',r'$\pi$'])   # 5 values in x_axis
plt.yticks([-1,-0.5,0,0.5,1],[r'$-1$',r'$-0.5$',r'$0$',r'$0.5$',r'$1$'])   # 5 values in y-axis#move the boundary line,set origin is 0
ax = plt.gca()  #get current line position
ax.xaxis.set_ticks_position('bottom')
ax.yaxis.set_ticks_position('left')
ax.spines['bottom'].set_position(('data', 0))  #set bottom position to 0
ax.spines['left'].set_position(('data', 0))
ax.spines['top'].set_color('none')      #cancel original boundary
ax.spines['right'].set_color('none')plt.plot(x, y, label = 'sin(x)')    #add label and show on the graph
plt.plot(x, z, label = 'cos(x)')
plt.legend(loc = 'upper left')plt.show()

去掉边框的正弦，余弦曲线图片如下：

1.3， python画正切函数曲线，我们在上述的正余弦曲线的代码中加入a = np.tan(x)的代码，同时需要区分正弦曲线，余弦曲线和正切曲线：

import numpy as np
from matplotlib import pyplot as plt plt.figure(figsize = (6, 8), dpi = 200) # create a frame, dpi = 200
plt.subplot(111)    #create a subgraph, grid = 1 * 1x = np.linspace(-np.pi, np.pi, 256, endpoint = True)  #numpy array:[-π, π], total 256 values
y = np.sin(x)
z = np.cos(x)
a = np.tan(x)plt.plot(x, y, color = 'blue', label = 'sin(x)',linewidth = 2.0, linestyle= '-')      #define line color and style
plt.plot(x, z, color = 'red', label = 'cos(x)', linewidth = 2.0, linestyle= '--')
plt.plot(x, a, color = 'yellow', label = 'tan(x)', linewidth = 2.0, linestyle= '-.')plt.xlim(x.min() * 1.1, x.max() * 1.1)     #limit x range
plt.ylim(y.min() * 1.1, y.max() * 1.1)     #limit y rangeplt.xticks([-np.pi,-np.pi/2,0,np.pi/2,np.pi],[r'$-\pi$',r'$-\pi/2$',r'$0$',r'$\pi/2$',r'$\pi$'])   # 5 values in x_axis
plt.yticks([-1,-0.5,0,0.5,1],[r'$-1$',r'$-0.5$',r'$0$',r'$0.5$',r'$1$'])   # 5 values in y-axis#move the boundary line,set origin is 0
ax = plt.gca()  #get current line position
ax.xaxis.set_ticks_position('bottom')
ax.yaxis.set_ticks_position('left')
ax.spines['bottom'].set_position(('data', 0))  #set bottom position to 0
ax.spines['left'].set_position(('data', 0))
ax.spines['top'].set_color('none')      #cancel original boundary
ax.spines['right'].set_color('none')plt.legend(loc = (0, 0.92))plt.show()

去掉边框的正弦，余弦，正切曲线图片如下：

1.4, 我们直接画出sin(x), cos(x), tan(x), cot(x)的函数曲线图吧

1.5， python画双曲正弦函数曲线，由于y的值域范围和正弦余弦函数不同，我们重新创建一个双曲正弦曲线画布：

import numpy as np
from matplotlib import pyplot as plt plt.figure(figsize = (6, 8), dpi = 200) # create a frame, dpi = 200
plt.subplot(111)    #create a subgraph, grid = 1 * 1x = np.linspace(-np.pi, np.pi, 256, endpoint = True)  #numpy array:[-π, π], total 256 values
y = np.sinh(x)plt.plot(x, y, color = 'blue', label = 'sinh(x)',linewidth = 2.0, linestyle= '-')      #define line color and styleplt.xlim(x.min() * 1.1, x.max() * 1.1)     #limit x range
plt.ylim(y.min() * 1.1, y.max() * 1.1)     #limit y rangeplt.xticks([-np.pi,-np.pi/2,0,np.pi/2,np.pi],[r'$-\pi$',r'$-\pi/2$',r'$0$',r'$\pi/2$',r'$\pi$'])   # 5 values in x_axis
plt.yticks([-10,-5,5,10],[r'$-10$',r'$-5$',r'$5$',r'$10$'])   # 4 values in y-axis#move the boundary line,set origin is 0
ax = plt.gca()  #get current line position
ax.xaxis.set_ticks_position('bottom')
ax.yaxis.set_ticks_position('left')
ax.spines['bottom'].set_position(('data', 0))  #set bottom position to 0
ax.spines['left'].set_position(('data', 0))
ax.spines['top'].set_color('none')      #cancel original boundary
ax.spines['right'].set_color('none')plt.legend(loc = 'upper left')plt.show()

去掉边框的双曲正弦曲线图片如下：

1.6， python画双曲余弦函数曲线，在双曲正弦函数曲线的画布基础上添加y = np.cosh(x), 同时区分两个函数曲线：

import numpy as np
from matplotlib import pyplot as plt plt.figure(figsize = (6, 8), dpi = 200) # create a frame, dpi = 200
plt.subplot(111)    #create a subgraph, grid = 1 * 1x = np.linspace(-np.pi, np.pi, 256, endpoint = True)  #numpy array:[-π, π], total 256 values
y = np.sinh(x)
z = np.cosh(x)plt.plot(x, y, color = 'blue', label = 'sinh(x)',linewidth = 2.0, linestyle= '-')      #define line color and style
plt.plot(x, z, color = 'red', label = 'cosh(x)', linewidth = 2.0, linestyle= '--')plt.xlim(x.min() * 1.1, x.max() * 1.1)     #limit x range
plt.ylim(y.min() * 1.1, y.max() * 1.1)     #limit y rangeplt.xticks([-np.pi,-np.pi/2,0,np.pi/2,np.pi],[r'$-\pi$',r'$-\pi/2$',r'$0$',r'$\pi/2$',r'$\pi$'])   # 5 values in x_axis
plt.yticks([-10,-5,5,10],[r'$-10$',r'$-5$',r'$5$',r'$10$'])   # 4 values in y-axis#move the boundary line,set origin is 0
ax = plt.gca()  #get current line position
ax.xaxis.set_ticks_position('bottom')
ax.yaxis.set_ticks_position('left')
ax.spines['bottom'].set_position(('data', 0))  #set bottom position to 0
ax.spines['left'].set_position(('data', 0))
ax.spines['top'].set_color('none')      #cancel original boundary
ax.spines['right'].set_color('none')plt.legend(loc = 'upper left')plt.show()

去掉边框的双曲正弦，双曲余弦曲线图片如下：

1.7， python画双曲正切函数曲线，在双曲正弦函数和双曲余弦函数曲线的画布基础上添加a = np.tanh(x), 同时区分三个函数曲线：

import numpy as np
from matplotlib import pyplot as plt plt.figure(figsize = (6, 8), dpi = 200) # create a frame, dpi = 200
plt.subplot(111)    #create a subgraph, grid = 1 * 1x = np.linspace(-np.pi, np.pi, 256, endpoint = True)  #numpy array:[-π, π], total 256 values
y = np.sinh(x)
z = np.cosh(x)
a = np.tanh(x)plt.plot(x, y, color = 'blue', label = 'sinh(x)',linewidth = 2.0, linestyle= '-')      #define line color and style
plt.plot(x, z, color = 'red', label = 'cosh(x)', linewidth = 2.0, linestyle= '--')
plt.plot(x, a, color = 'purple', label = 'tanh(x)', linewidth = 2.0, linestyle= '-.')plt.xlim(x.min() * 1.1, x.max() * 1.1)     #limit x range
plt.ylim(y.min() * 1.1, y.max() * 1.1)     #limit y rangeplt.xticks([-np.pi,-np.pi/2,0,np.pi/2,np.pi],[r'$-\pi$',r'$-\pi/2$',r'$0$',r'$\pi/2$',r'$\pi$'])   # 5 values in x_axis
plt.yticks([-10,-5,5,10],[r'$-10$',r'$-5$',r'$5$',r'$10$'])   # 4 values in y-axis#move the boundary line,set origin is 0
ax = plt.gca()  #get current line position
ax.xaxis.set_ticks_position('bottom')
ax.yaxis.set_ticks_position('left')
ax.spines['bottom'].set_position(('data', 0))  #set bottom position to 0
ax.spines['left'].set_position(('data', 0))
ax.spines['top'].set_color('none')      #cancel original boundary
ax.spines['right'].set_color('none')plt.legend(loc = 'upper left')plt.show()

去掉边框的双曲正弦，双曲余弦，双曲正切曲线图片如下：

1.8，我们再直接画出sinh(x), cosh(x), tanh(x)和coth(x)的函数曲线图吧。

1.9 python画反正弦函数曲线，我们再重新创建一个反正弦曲线画布，注意x轴和y轴是等比例的：

import numpy as np
from matplotlib import pyplot as plt plt.figure(figsize = (6, 8), dpi = 200) # create a frame, dpi = 200
plt.subplot(111)    #create a subgraph, grid = 1 * 1x = np.linspace(-1, 1, 1000, endpoint = True)  #x range changed
y = np.arcsin(x)plt.plot(x, y, color = 'blue', label = 'arcsin(x)',linewidth = 1.0, linestyle= '-')      #define line color and styleplt.xlim(-1, 1)     #limit x range
plt.ylim(-np.pi/2, np.pi/2)     #limit y rangeplt.xticks([-1,-0.5,0,0.5,1],[r'$-1$',r'$-0.5$',r'$0$',r'$0.5$',r'$1$'])   # 5 values in x-axis
plt.yticks([-np.pi/2, -0.75, 0.75, np.pi/2],[r'$-\pi/2$',r'$-0.75$',r'$0.75$',r'$\pi/2$'])   # 4 values in y_axis#move the boundary line,set origin is 0
plt.axis('equal')       #x-axis and y-axis scale equally
ax = plt.gca()  #get current line position
ax.xaxis.set_ticks_position('bottom')
ax.yaxis.set_ticks_position('left')
ax.spines['bottom'].set_position(('data', 0))  #set bottom position to 0
ax.spines['left'].set_position(('data', 0))
ax.spines['top'].set_color('none')      #cancel original boundary
ax.spines['right'].set_color('none')plt.legend(loc = 'upper left')plt.show()

去掉边框的反正弦曲线函数：

1.10, python画反余弦函数曲线，我们在反正弦曲线画布基础上增加，注意x轴和y轴是等比例的：

import numpy as np
from matplotlib import pyplot as plt plt.figure(figsize = (6, 8), dpi = 200) # create a frame, dpi = 200
plt.subplot(111)    #create a subgraph, grid = 1 * 1x = np.linspace(-1, 1, 1000, endpoint = True)   # x range changed
y = np.arcsin(x)
z = np.arccos(x)plt.plot(x, y, color = 'blue', label = 'arcsin(x)',linewidth = 1.0, linestyle= '-')      #define line color and style
plt.plot(x, z, color = 'red', label = 'arccos(x)',linewidth = 1.0, linestyle= '--') plt.xlim(-1, 1)     #limit x range
plt.ylim(-np.pi/2, np.pi/2)     #limit y rangeplt.xticks([-1,-0.5,0,0.5,1],[r'$-1$',r'$-0.5$',r'$0$',r'$0.5$',r'$1$'])   # 5 values in x-axis
plt.yticks([-np.pi/2, -0.75, 0.75, np.pi/2],[r'$-\pi/2$',r'$-0.75$',r'$0.75$',r'$\pi/2$'])   # 4 values in y_axis#move the boundary line,set origin is 0
plt.axis('equal')       #x-axis and y-axis scale equally
ax = plt.gca()  #get current line position
ax.xaxis.set_ticks_position('bottom')
ax.yaxis.set_ticks_position('left')
ax.spines['bottom'].set_position(('data', 0))  #set bottom position to 0
ax.spines['left'].set_position(('data', 0))
ax.spines['top'].set_color('none')      #cancel original boundary
ax.spines['right'].set_color('none')plt.legend(loc = 'upper left')plt.show()

去掉边框的反正弦，反余弦函数曲线函数：

1.11, python画反正切函数曲线，我们在反正弦曲线和反余弦曲线画布基础上增加，注意x轴和y轴是等比例的：

import numpy as np
from matplotlib import pyplot as plt plt.figure(figsize = (6, 8), dpi = 200) # create a frame, dpi = 200
plt.subplot(111)    #create a subgraph, grid = 1 * 1x = np.linspace(-1, 1, 1000, endpoint = True)   # x range changed
y = np.arcsin(x)
z = np.arccos(x)
a = np.arctan(x)plt.plot(x, y, color = 'blue', label = 'arcsin(x)',linewidth = 1.0, linestyle= '-')      #define line color and style
plt.plot(x, z, color = 'red', label = 'arccos(x)',linewidth = 1.0, linestyle= '--')
plt.plot(x, a, color = 'purple', label = 'arctan(x)', linewidth = 1.0, linestyle= '-.')plt.xlim(-1, 1)     #limit x range
plt.ylim(-np.pi/2, np.pi/2)     #limit y rangeplt.xticks([-1,-0.5,0,0.5,1],[r'$-1$',r'$-0.5$',r'$0$',r'$0.5$',r'$1$'])   # 5 values in x-axis
plt.yticks([-np.pi/2, -0.75, 0.75, np.pi/2],[r'$-\pi/2$',r'$-0.75$',r'$0.75$',r'$\pi/2$'])   # 4 values in y_axis#move the boundary line,set origin is 0
plt.axis('equal')       #x-axis and y-axis scale equally
ax = plt.gca()  #get current line position
ax.xaxis.set_ticks_position('bottom')
ax.yaxis.set_ticks_position('left')
ax.spines['bottom'].set_position(('data', 0))  #set bottom position to 0
ax.spines['left'].set_position(('data', 0))
ax.spines['top'].set_color('none')      #cancel original boundary
ax.spines['right'].set_color('none')plt.legend(loc = 'upper left')plt.show()

去掉边框的反正弦，反余弦函数，反正切函数曲线函数：

1.12，我们再直接画出arcsin(x), arccos(x), arctan(x)和arccot(x)的函数曲线图吧。

1.13，最后还有反双曲正弦，反双曲余弦，反双曲正切，反双曲余切函数曲线，留给大家自己去发挥吧，注意x和y的值域。

最后，祝大家学习快乐，转载请注明出处。

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python中内置数学函数详解和实例应用之三角函数曲线_初级阶段（三）

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python中内置数学函数详解和实例应用之三角函数曲线_初级阶段（三）相关推荐

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