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

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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 npfrom matplotlib import pyplot as plt plt.figure(figsize = (6, 8), dpi = 200) # create a frame, dpi = 200plt.subplot(111) #create a subgraph, grid = 1 * 1x = np.linspace(-np.pi, np.pi, 256, endpoint = True) #numpy array:[-π, π], total 256 valuesy = 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 rangeplt.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_axisplt.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 npfrom matplotlib import pyplot as plt plt.figure(figsize = (6, 8), dpi = 200) # create a frame, dpi = 200plt.subplot(111) #create a subgraph, grid = 1 * 1x = np.linspace(-np.pi, np.pi, 256, endpoint = True) #numpy array:[-π, π], total 256 valuesy = 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 rangeplt.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_axisplt.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 0ax = plt.gca() #get current line positionax.xaxis.set_ticks_position('bottom') ax.yaxis.set_ticks_position('left')ax.spines['bottom'].set_position(('data', 0)) #set bottom position to 0ax.spines['left'].set_position(('data', 0))ax.spines['top'].set_color('none')#cancel original boundaryax.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 npfrom matplotlib import pyplot as plt plt.figure(figsize = (6, 8), dpi = 200) # create a frame, dpi = 200plt.subplot(111) #create a subgraph, grid = 1 * 1x = np.linspace(-np.pi, np.pi, 256, endpoint = True) #numpy array:[-π, π], total 256 valuesy = np.sin(x)z = np.cos(x)plt.plot(x, y, color = 'blue', linewidth = 2.0, linestyle= '-')#define line color and styleplt.plot(x, z, color = 'red', linewidth = 2.0, linestyle= '-')plt.xlim(x.min() * 1.1, x.max() * 1.1)#limit x rangeplt.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_axisplt.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 0ax = plt.gca() #get current line positionax.xaxis.set_ticks_position('bottom') ax.yaxis.set_ticks_position('left')ax.spines['bottom'].set_position(('data', 0)) #set bottom position to 0ax.spines['left'].set_position(('data', 0))ax.spines['top'].set_color('none')#cancel original boundaryax.spines['right'].set_color('none')plt.plot(x, y, label = 'sin(x)') #add label and show on the graphplt.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 npfrom matplotlib import pyplot as plt plt.figure(figsize = (6, 8), dpi = 200) # create a frame, dpi = 200plt.subplot(111) #create a subgraph, grid = 1 * 1x = np.linspace(-np.pi, np.pi, 256, endpoint = True) #numpy array:[-π, π], total 256 valuesy = 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 styleplt.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 rangeplt.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_axisplt.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 0ax = plt.gca() #get current line positionax.xaxis.set_ticks_position('bottom') ax.yaxis.set_ticks_position('left')ax.spines['bottom'].set_position(('data', 0)) #set bottom position to 0ax.spines['left'].set_position(('data', 0))ax.spines['top'].set_color('none')#cancel original boundaryax.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 npfrom matplotlib import pyplot as plt plt.figure(figsize = (6, 8), dpi = 200) # create a frame, dpi = 200plt.subplot(111) #create a subgraph, grid = 1 * 1x = np.linspace(-np.pi, np.pi, 256, endpoint = True) #numpy array:[-π, π], total 256 valuesy = 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 rangeplt.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_axisplt.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 0ax = plt.gca() #get current line positionax.xaxis.set_ticks_position('bottom') ax.yaxis.set_ticks_position('left')ax.spines['bottom'].set_position(('data', 0)) #set bottom position to 0ax.spines['left'].set_position(('data', 0))ax.spines['top'].set_color('none')#cancel original boundaryax.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 npfrom matplotlib import pyplot as plt plt.figure(figsize = (6, 8), dpi = 200) # create a frame, dpi = 200plt.subplot(111) #create a subgraph, grid = 1 * 1x = np.linspace(-np.pi, np.pi, 256, endpoint = True) #numpy array:[-π, π], total 256 valuesy = np.sinh(x)z = np.cosh(x)plt.plot(x, y, color = 'blue', label = 'sinh(x)',linewidth = 2.0, linestyle= '-')#define line color and styleplt.plot(x, z, color = 'red', label = 'cosh(x)', linewidth = 2.0, linestyle= '--')plt.xlim(x.min() * 1.1, x.max() * 1.1)#limit x rangeplt.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_axisplt.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 0ax = plt.gca() #get current line positionax.xaxis.set_ticks_position('bottom') ax.yaxis.set_ticks_position('left')ax.spines['bottom'].set_position(('data', 0)) #set bottom position to 0ax.spines['left'].set_position(('data', 0))ax.spines['top'].set_color('none')#cancel original boundaryax.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 npfrom matplotlib import pyplot as plt plt.figure(figsize = (6, 8), dpi = 200) # create a frame, dpi = 200plt.subplot(111) #create a subgraph, grid = 1 * 1x = np.linspace(-np.pi, np.pi, 256, endpoint = True) #numpy array:[-π, π], total 256 valuesy = 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 styleplt.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 rangeplt.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_axisplt.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 0ax = plt.gca() #get current line positionax.xaxis.set_ticks_position('bottom') ax.yaxis.set_ticks_position('left')ax.spines['bottom'].set_position(('data', 0)) #set bottom position to 0ax.spines['left'].set_position(('data', 0))ax.spines['top'].set_color('none')#cancel original boundaryax.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 npfrom matplotlib import pyplot as plt plt.figure(figsize = (6, 8), dpi = 200) # create a frame, dpi = 200plt.subplot(111) #create a subgraph, grid = 1 * 1x = np.linspace(-1, 1, 1000, endpoint = True) #x range changedy = 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 rangeplt.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-axisplt.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 0plt.axis('equal') #x-axis and y-axis scale equallyax = plt.gca() #get current line positionax.xaxis.set_ticks_position('bottom') ax.yaxis.set_ticks_position('left')ax.spines['bottom'].set_position(('data', 0)) #set bottom position to 0ax.spines['left'].set_position(('data', 0))ax.spines['top'].set_color('none')#cancel original boundaryax.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 npfrom matplotlib import pyplot as plt plt.figure(figsize = (6, 8), dpi = 200) # create a frame, dpi = 200plt.subplot(111) #create a subgraph, grid = 1 * 1x = np.linspace(-1, 1, 1000, endpoint = True) # x range changedy = np.arcsin(x)z = np.arccos(x)plt.plot(x, y, color = 'blue', label = 'arcsin(x)',linewidth = 1.0, linestyle= '-')#define line color and styleplt.plot(x, z, color = 'red', label = 'arccos(x)',linewidth = 1.0, linestyle= '--') plt.xlim(-1, 1)#limit x rangeplt.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-axisplt.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 0plt.axis('equal') #x-axis and y-axis scale equallyax = plt.gca() #get current line positionax.xaxis.set_ticks_position('bottom') ax.yaxis.set_ticks_position('left')ax.spines['bottom'].set_position(('data', 0)) #set bottom position to 0ax.spines['left'].set_position(('data', 0))ax.spines['top'].set_color('none')#cancel original boundaryax.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 npfrom matplotlib import pyplot as plt plt.figure(figsize = (6, 8), dpi = 200) # create a frame, dpi = 200plt.subplot(111) #create a subgraph, grid = 1 * 1x = np.linspace(-1, 1, 1000, endpoint = True) # x range changedy = 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 styleplt.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 rangeplt.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-axisplt.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 0plt.axis('equal') #x-axis and y-axis scale equallyax = plt.gca() #get current line positionax.xaxis.set_ticks_position('bottom') ax.yaxis.set_ticks_position('left')ax.spines['bottom'].set_position(('data', 0)) #set bottom position to 0ax.spines['left'].set_position(('data', 0))ax.spines['top'].set_color('none')#cancel original boundaryax.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。