Python笔记之用turtle库绘制三角函数和反三角函数的图像(考研党福利)

文章目录

前言

最近因为复习高数在网上找三角函数图像,发现大多数都模糊不清,实在是头痛,所以自己学以致用,用Python画出了三角函数图像。希望我的博客可以帮到大家,也祝考研党们早日上岸,考上理想的学校!
想了解代码的详细信息可以去看我的另一篇博客:
https://blog.csdn.net/qq_44437695/article/details/104762815

程序源代码

from math import *
from tkinter import mainloop
from turtle import *


# 画出坐标轴
def axis(t):
    s = Screen()
    s.setworldcoordinates(-4, -4, 4, 4)
    t.speed(0)
    s.delay(0)
    t.goto(-4, 0)
    for i in range(-4, 4):
        t.write(i, False, "right", ("Arial", 12, "normal"))
        t.fd(1)
    t.stamp()
    t.write("x", False, "center", ("Arial", 20, "normal"))
    t.penup()
    t.goto(0, -4)
    t.pendown()
    t.left(90)
    for i in range(-4, 4):
        t.write(i, False, "right", ("Arial", 12, "normal"))
        t.fd(1)
    t.write("y", False, "center", ("Arial", 20, "normal"))
    t.stamp()
    t.penup()
    t.hideturtle()


# 三角函数的sin(x)、arcsin(x)、cos(x)、arccos(x)、tan(x)、arctan(x)均可以用math库调用

# 余切函数cot(x)
def cot(x):
    if tan(x) != 0:
        return 1 / tan(x)
    else:
        exit("x取值不在定义域内!")


# 反余切函数arccot(x)
def acot(x):
    if x > 0:
        return atan(1 / x)
    elif x < 0:
        return pi + atan(1 / x)
    else:
        return pi / 2


# 正割函数sec(x)
def sec(x):
    if cos(x) != 0:
        return 1 / cos(x)
    else:
        exit("x取值不在定义域内!")


# 反正割函数arcsec(x)
def asec(x):
    if x >= 1:
        return atan(sqrt(pow(x, 2) - 1))
    elif x <= -1:
        return pi - atan(sqrt(pow(x, 2) - 1))
    else:
        exit("x取值不在定义域内!")


# 余割函数csc(x)
def csc(x):
    if sin(x) != 0:
        return 1 / sin(x)
    else:
        exit("x取值不在定义域内!")


# 反余割函数arccsc(x)
def acsc(x):
    if x >= 1:
        return acot(sqrt(pow(x, 2) - 1))
    elif x <= -1:
        return 0 - acot(sqrt(pow(x, 2) - 1))
    else:
        exit("x取值不在定义域内!")


# 在坐标轴上画出正弦函数sin(x)图像
def sin_draw():
    t = Turtle()
    axis(t)
    t.goto(-4, 4)
    t.write("正弦函数sin(x)图像", False, "center", ("Arial", 20, "normal"))
    t.color("blue")
    t.goto(3 * pi / 2, -1)
    t.write("(3*π/2,-1)", False, "center", ("Arial", 15, "normal"))
    t.goto(pi, 0)
    t.write("(π,0)", False, "left", ("Arial", 15, "normal"))
    t.goto(pi / 2, 1)
    t.write("(π/2,1)", False, "center", ("Arial", 15, "normal"))
    t.goto(0, 0)
    t.write("(0,0)", False, "left", ("Arial", 15, "normal"))
    t.goto(-pi / 2, -1)
    t.write("(-π/2,-1)", False, "center", ("Arial", 15, "normal"))
    t.goto(-pi, 0)
    t.write("(-π,0)", False, "right", ("Arial", 15, "normal"))
    t.goto(-3 * pi / 2, 1)
    t.write("(-3*π/2,1)", False, "center", ("Arial", 15, "normal"))
    t.color("black")
    t.pendown()
    for i in range(-5000, 5000):
        x = 0.001 * i
        t.goto(x, sin(x))


# 在坐标轴上画出反正弦函数asin(x)图像
def asin_draw():
    t = Turtle()
    axis(t)
    t.goto(-4, 4)
    t.write("反正弦函数asin(x)图像", False, "center", ("Arial", 20, "normal"))
    t.color("blue")
    t.goto(1, pi / 2)
    t.write("(1,π/2)", False, "left", ("Arial", 15, "normal"))
    t.goto(-1, -pi / 2)
    t.write("(-1,-π/2)", False, "right", ("Arial", 15, "normal"))
    t.color("black")
    t.pendown()
    for i in range(-1000, 1000):
        x = 0.001 * i
        t.goto(x, asin(x))
    t_line = Turtle()
    t_line.hideturtle()
    t_line.color("green")
    t_line.speed(0)
    t_line.penup()
    t_line.goto(0, pi / 2)
    t_line.pendown()
    t_line.fd(1)
    t_line.right(90)
    t_line.fd(pi / 2)
    t_line.penup()
    t_line.goto(-1, 0)
    t_line.pendown()
    t_line.fd(pi / 2)
    t_line.left(90)
    t_line.fd(1)


# 在坐标轴上画出余弦函数cos(x)图像
def cos_draw():
    t = Turtle()
    axis(t)
    t.goto(-4, 4)
    t.write("余弦函数cos(x)图像", False, "center", ("Arial", 20, "normal"))
    t.color("blue")
    t.goto(3 * pi / 2, 0)
    t.write("(3*π/2,0)", False, "center", ("Arial", 15, "normal"))
    t.goto(pi, -1)
    t.write("(π,-1)", False, "left", ("Arial", 15, "normal"))
    t.goto(pi / 2, 0)
    t.write("(π/2,0)", False, "center", ("Arial", 15, "normal"))
    t.goto(0, 1)
    t.write("(0,1)", False, "left", ("Arial", 15, "normal"))
    t.goto(-pi / 2, 0)
    t.write("(-π/2,0)", False, "center", ("Arial", 15, "normal"))
    t.goto(-pi, -1)
    t.write("(-π,-1)", False, "right", ("Arial", 15, "normal"))
    t.goto(-3 * pi / 2, 0)
    t.write("(-3*π/2,0)", False, "center", ("Arial", 15, "normal"))
    t.color("black")
    t.pendown()
    for i in range(-5000, 5000):
        x = 0.001 * i
        t.goto(x, cos(x))


# 在坐标轴上画出反余弦函数acos(x)图像
def acos_draw():
    t = Turtle()
    axis(t)
    t.goto(-4, 4)
    t.write("反余弦函数acos(x)图像", False, "center", ("Arial", 20, "normal"))
    t.color("blue")
    t.goto(1, 0)
    t.write("(1,0)", False, "left", ("Arial", 15, "normal"))
    t.goto(-1, pi)
    t.write("(-1,π)", False, "right", ("Arial", 15, "normal"))
    t.color("black")
    t.pendown()
    for i in range(-1000, 1000):
        x = 0.001 * i
        t.goto(x, acos(x))
    t_line = Turtle()
    t_line.hideturtle()
    t_line.color("green")
    t_line.speed(0)
    t_line.penup()
    t_line.goto(-1, 0)
    t_line.pendown()
    t_line.left(90)
    t_line.fd(pi)
    t_line.right(90)
    t_line.fd(1)


# 在坐标轴上画出正切函数tan(x)图像
def tan_draw():
    t = Turtle()
    axis(t)
    t.goto(-4, 4)
    t.write("正切函数tan(x)图像", False, "center", ("Arial", 20, "normal"))
    t.color("blue")
    t.goto(-pi, 0)
    t.write("(-π,0)", False, "right", ("Arial", 15, "normal"))
    t.goto(0, 0)
    t.write("(0,0)", False, "left", ("Arial", 15, "normal"))
    t.goto(pi, 0)
    t.write("(π,0)", False, "left", ("Arial", 15, "normal"))
    t.color("black")
    t.goto(-4.467, tan(-4.467))
    t.pendown()
    for i in range(-4467, -1817):
        x = 0.001 * i
        t.goto(x, tan(x))
    t.penup()
    t.goto(-1.325, tan(-1.325))
    t.pendown()
    for i in range(-1325, 1329):
        x = 0.001 * i
        t.goto(x, tan(x))
    t.penup()
    t.goto(1.817, tan(1.817))
    t.pendown()
    for i in range(1817, 4467):
        x = 0.001 * i
        t.goto(x, tan(x))
    t_line = Turtle()
    t_line.hideturtle()
    t_line.color("green")
    t_line.speed(0)
    t_line.penup()
    t_line.goto(-pi / 2, -4)
    t_line.write("渐近线x=-π/2", False, "right", ("Arial", 20, "normal"))
    t_line.pendown()
    t_line.left(90)
    t_line.fd(8)
    t_line.penup()
    t_line.goto(pi / 2, -4)
    t_line.write("渐近线x=π/2", False, "right", ("Arial", 20, "normal"))
    t_line.pendown()
    t_line.fd(8)


# 在坐标轴上画出反正切函数arctan(x)图像
def atan_draw():
    t = Turtle()
    axis(t)
    t.goto(-4, 4)
    t.write("反正切函数arctan(x)图像", False, "center", ("Arial", 20, "normal"))
    t.goto(-5, atan(-5))
    t.pendown()
    for i in range(-5000, 5000):
        x = 0.001 * i
        t.goto(x, atan(x))
    t_line = Turtle()
    t_line.hideturtle()
    t_line.color("green")
    t_line.speed(0)
    t_line.penup()
    t_line.goto(-5, pi / 2)
    t_line.write("渐近线y=π/2", False, "right", ("Arial", 20, "normal"))
    t_line.pendown()
    t_line.fd(10)
    t_line.penup()
    t_line.goto(-5, -pi / 2)
    t_line.write("渐近线y=-π/2", False, "right", ("Arial", 20, "normal"))
    t_line.pendown()
    t_line.fd(10)


# 在坐标轴上画出余切函数cot(x)图像
def cot_draw():
    t = Turtle()
    axis(t)
    t.goto(-4, 4)
    t.write("余切函数cot(x)图像", False, "center", ("Arial", 20, "normal"))
    t.color("blue")
    t.goto(-3 * pi / 2, 0)
    t.write("(-3*π/2,0)", False, "center", ("Arial", 15, "normal"))
    t.goto(-pi / 2, 0)
    t.write("(-π/2,0)", False, "center", ("Arial", 15, "normal"))
    t.goto(pi / 2, 0)
    t.write("(π/2,0)", False, "center", ("Arial", 15, "normal"))
    t.goto(3 * pi / 2, 0)
    t.write("(3*π/2,0)", False, "center", ("Arial", 15, "normal"))
    t.color("black")
    t.goto(-6.038, cot(-6.038))
    t.pendown()
    for i in range(-6038, -3388):
        x = 0.001 * i
        t.goto(x, cot(x))
    t.penup()
    t.goto(-2.896, cot(-2.896))
    t.pendown()
    for i in range(-2896, -246):
        x = 0.001 * i
        t.goto(x, cot(x))
    t.penup()
    t.goto(0.246, cot(0.246))
    t.pendown()
    for i in range(246, 2896):
        x = 0.001 * i
        t.goto(x, cot(x))
    t.penup()
    t.goto(3.388, cot(3.388))
    t.pendown()
    for i in range(3388, 6038):
        x = 0.001 * i
        t.goto(x, cot(x))
    t_line = Turtle()
    t_line.hideturtle()
    t_line.color("green")
    t_line.speed(0)
    t_line.penup()
    t_line.goto(-pi, -4)
    t_line.write("渐近线x=-π", False, "left", ("Arial", 20, "normal"))
    t_line.pendown()
    t_line.left(90)
    t_line.fd(8)
    t_line.penup()
    t_line.goto(0, -4)
    t_line.write("渐近线x=0", False, "left", ("Arial", 20, "normal"))
    t_line.pendown()
    t_line.fd(8)
    t_line.penup()
    t_line.goto(pi, -4)
    t_line.write("渐近线x=π", False, "left", ("Arial", 20, "normal"))
    t_line.pendown()
    t_line.fd(8)


# 在坐标轴上画出反余切函数arccot(x)图像
def acot_draw():
    t = Turtle()
    axis(t)
    t.goto(-4, 4)
    t.write("反余切函数arccot(x)图像", False, "center", ("Arial", 20, "normal"))
    t.color("blue")
    t.goto(0, pi / 2)
    t.write("(0,π/2)", False, "left", ("Arial", 15, "normal"))
    t.color("black")
    t.goto(-5, acot(-5))
    t.pendown()
    for i in range(-5000, 5000):
        x = 0.001 * i
        t.goto(x, acot(x))
    t_line = Turtle()
    t_line.hideturtle()
    t_line.color("green")
    t_line.speed(0)
    t_line.penup()
    t_line.goto(-5, pi)
    t_line.write("渐近线y=π", False, "right", ("Arial", 20, "normal"))
    t_line.pendown()
    t_line.fd(10)
    t_line.penup()
    t_line.goto(-5, 0)
    t_line.write("渐近线y=0", False, "right", ("Arial", 20, "normal"))
    t_line.pendown()
    t_line.fd(10)


# 在坐标轴上画出正割函数sec(x)图像
def sec_draw():
    t = Turtle()
    axis(t)
    t.goto(-4, 4)
    t.write("正割函数sec(x)图像", False, "center", ("Arial", 20, "normal"))
    t.color("blue")
    t.goto(0, 1)
    t.write("(0,1)", False, "left", ("Arial", 15, "normal"))
    t.goto(-pi, -1)
    t.write("(-π,-1)", False, "center", ("Arial", 15, "normal"))
    t.goto(pi, -1)
    t.write("(π,-1)", False, "center", ("Arial", 15, "normal"))
    t.color("black")
    t.goto(-4.467, sec(-4.467))
    t.pendown()
    for i in range(-4467, -1817):
        x = 0.001 * i
        t.goto(x, sec(x))
    t.penup()
    t.goto(-1.325, sec(-1.325))
    t.pendown()
    for i in range(-1325, 1329):
        x = 0.001 * i
        t.goto(x, sec(x))
    t.penup()
    t.goto(1.817, sec(1.817))
    t.pendown()
    for i in range(1817, 4467):
        x = 0.001 * i
        t.goto(x, sec(x))
    t_line = Turtle()
    t_line.hideturtle()
    t_line.color("green")
    t_line.speed(0)
    t_line.penup()
    t_line.goto(-pi / 2, -4)
    t_line.write("渐近线x=-π/2", False, "right", ("Arial", 20, "normal"))
    t_line.pendown()
    t_line.left(90)
    t_line.fd(8)
    t_line.penup()
    t_line.goto(pi / 2, -4)
    t_line.write("渐近线x=π/2", False, "right", ("Arial", 20, "normal"))
    t_line.pendown()
    t_line.fd(8)
    t_line.right(90)
    t_line.penup()
    t_line.goto(-5, 1)
    t_line.write("y=1", False, "right", ("Arial", 20, "normal"))
    t_line.pendown()
    t_line.fd(10)
    t_line.penup()
    t_line.goto(-5, -1)
    t_line.write("y=-1", False, "right", ("Arial", 20, "normal"))
    t_line.pendown()
    t_line.fd(10)


# 在坐标轴上画出反正割函数arcsec(x)图像
def asec_draw():
    t = Turtle()
    axis(t)
    t.goto(-4, 4)
    t.write("反正割函数arcsec(x)图像", False, "center", ("Arial", 20, "normal"))
    t.color("blue")
    t.goto(1, 0)
    t.write("(1,0)", False, "left", ("Arial", 15, "normal"))
    t.color("black")
    t.pendown()
    for i in range(1000, 5000):
        x = 0.001 * i
        t.goto(x, asec(x))
    t.penup()
    t.color("blue")
    t.goto(-1, pi)
    t.write("(-1,π)", False, "right", ("Arial", 15, "normal"))
    t.color("black")
    t.pendown()
    for i in range(-1000, -5000, -1):
        x = 0.001 * i
        t.goto(x, asec(x))
    t_line = Turtle()
    t_line.hideturtle()
    t_line.color("green")
    t_line.speed(0)
    t_line.penup()
    t_line.goto(-1, 0)
    t_line.pendown()
    t_line.left(90)
    t_line.fd(pi)
    t_line.right(90)
    t_line.fd(1)
    t_line.penup()
    t_line.goto(-5, pi / 2)
    t_line.write("渐近线y=π/2", False, "right", ("Arial", 20, "normal"))
    t_line.pendown()
    t_line.fd(10)


# 在坐标轴上画出余割函数csc(x)图像
def csc_draw():
    t = Turtle()
    axis(t)
    t.goto(-4, 4)
    t.write("余割函数csc(x)图像", False, "center", ("Arial", 20, "normal"))
    t.color("blue")
    t.goto(-3 * pi / 2, 1)
    t.write("(-3*π/2,1)", False, "left", ("Arial", 15, "normal"))
    t.goto(-pi / 2, -1)
    t.write("(-π/2,-1)", False, "center", ("Arial", 15, "normal"))
    t.goto(pi / 2, 1)
    t.write("(π/2,1)", False, "center", ("Arial", 15, "normal"))
    t.goto(3 * pi / 2, -1)
    t.write("(3*π/2,-1)", False, "center", ("Arial", 15, "normal"))
    t.color("black")
    t.goto(-6.038, csc(-6.038))
    t.pendown()
    for i in range(-6038, -3388):
        x = 0.001 * i
        t.goto(x, csc(x))
    t.penup()
    t.goto(-2.896, csc(-2.896))
    t.pendown()
    for i in range(-2896, -246):
        x = 0.001 * i
        t.goto(x, csc(x))
    t.penup()
    t.goto(0.246, csc(0.246))
    t.pendown()
    for i in range(246, 2896):
        x = 0.001 * i
        t.goto(x, csc(x))
    t.penup()
    t.goto(3.388, csc(3.388))
    t.pendown()
    for i in range(3388, 6038):
        x = 0.001 * i
        t.goto(x, csc(x))
    t_line = Turtle()
    t_line.hideturtle()
    t_line.color("green")
    t_line.speed(0)
    t_line.penup()
    t_line.goto(-pi, -4)
    t_line.write("渐近线x=-π", False, "left", ("Arial", 20, "normal"))
    t_line.pendown()
    t_line.left(90)
    t_line.fd(8)
    t_line.penup()
    t_line.goto(0, -4)
    t_line.write("渐近线x=0", False, "left", ("Arial", 20, "normal"))
    t_line.pendown()
    t_line.fd(8)
    t_line.penup()
    t_line.goto(pi, -4)
    t_line.write("渐近线x=π", False, "left", ("Arial", 20, "normal"))
    t_line.pendown()
    t_line.fd(8)
    t_line.right(90)
    t_line.penup()
    t_line.goto(-5, 1)
    t_line.write("y=1", False, "right", ("Arial", 20, "normal"))
    t_line.pendown()
    t_line.fd(10)
    t_line.penup()
    t_line.goto(-5, -1)
    t_line.write("y=-1", False, "right", ("Arial", 20, "normal"))
    t_line.pendown()
    t_line.fd(10)


# 在坐标轴上画出反余割函数arccsc(x)图像
def acsc_draw():
    t = Turtle()
    axis(t)
    t.goto(-4, 4)
    t.write("反余割函数arccsc(x)图像", False, "center", ("Arial", 20, "normal"))
    t.color("blue")
    t.goto(1, pi / 2)
    t.write("(1,π/2)", False, "left", ("Arial", 15, "normal"))
    t.color("black")
    t.pendown()
    for i in range(1000, 5000):
        x = 0.001 * i
        t.goto(x, acsc(x))
    t.penup()
    t.color("blue")
    t.goto(-1, -pi / 2)
    t.write("(-1,-π/2)", False, "right", ("Arial", 15, "normal"))
    t.color("black")
    t.pendown()
    for i in range(-1000, -5000, -1):
        x = 0.001 * i
        t.goto(x, acsc(x))
    t_line = Turtle()
    t_line.hideturtle()
    t_line.color("green")
    t_line.speed(0)
    t_line.penup()
    t_line.goto(0, pi / 2)
    t_line.pendown()
    t_line.fd(1)
    t_line.right(90)
    t_line.fd(pi / 2)
    t_line.right(90)
    t_line.fd(2)
    t_line.left(90)
    t_line.fd(pi / 2)
    t_line.left(90)
    t_line.fd(1)
    t_line.penup()
    t_line.goto(-5, 0)
    t_line.write("渐近线y=0", False, "right", ("Arial", 20, "normal"))
    t_line.pendown()
    t_line.fd(10)


if __name__ == '__main__':
    sin_draw()
    mainloop()

函数图像

sin(x)图像

《Python笔记之用turtle库绘制三角函数和反三角函数的图像(考研党福利)》

arcsin(x)图像

《Python笔记之用turtle库绘制三角函数和反三角函数的图像(考研党福利)》

cos(x)图像

《Python笔记之用turtle库绘制三角函数和反三角函数的图像(考研党福利)》

arccos(x)图像

《Python笔记之用turtle库绘制三角函数和反三角函数的图像(考研党福利)》

tan(x)图像

《Python笔记之用turtle库绘制三角函数和反三角函数的图像(考研党福利)》

arctan(x)图像

《Python笔记之用turtle库绘制三角函数和反三角函数的图像(考研党福利)》

cot(x)图像

《Python笔记之用turtle库绘制三角函数和反三角函数的图像(考研党福利)》

arccot(x)图像

《Python笔记之用turtle库绘制三角函数和反三角函数的图像(考研党福利)》

sec(x)图像

《Python笔记之用turtle库绘制三角函数和反三角函数的图像(考研党福利)》

arcsec(x)图像

《Python笔记之用turtle库绘制三角函数和反三角函数的图像(考研党福利)》

csc(x)图像

《Python笔记之用turtle库绘制三角函数和反三角函数的图像(考研党福利)》

arccsc(x)图像

《Python笔记之用turtle库绘制三角函数和反三角函数的图像(考研党福利)》

    原文作者:上轩希言
    原文地址: https://blog.csdn.net/qq_44437695/article/details/104901007
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