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Given the following text description, write Python code to implement the functionality described below step by step
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Description:
 Interact Exercise 2
Imports
Step1:  Plotting with parameters
Write a plot_sin1(a, b) function that plots $sin(ax+b)$ over the interval $[0,4\pi]$.
Customize your visualization to make it effective and beautiful.
Customize the box, grid, spines and ticks to match the requirements of this data.
Use enough points along the x-axis to get a smooth plot.
For the x-axis tick locations use integer multiples of $\pi$.
For the x-axis tick labels use multiples of pi using LaTeX
Step2:  Then use interact to create a user interface for exploring your function
Step3:  In matplotlib, the line style and color can be set with a third argument to plot. Examples of this argument
Step4:  Use interact to create a UI for plot_sine2.
Use a slider for a and b as above.
Use a drop down menu for selecting the line style between a dotted blue line line, black circles and red triangles.
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Python Code:
%matplotlib inline
from matplotlib import pyplot as plt
import numpy as np
from IPython.html.widgets import interact, interactive, fixed
from IPython.display import display
Explanation: Interact Exercise 2
Imports
End of explanation
# YOUR CODE HERE
def plot_sine1(a, b):
    t = np.linspace(0,4*np.pi,400)
    plt.plot(t,np.sin(a*t + b))
    plt.xlim(0,4*np.pi)
    plt.ylim(-1.0,1.0)
    plt.xticks([0,np.pi,2*np.pi,3*np.pi,4*np.pi], ['0','π','2π','3π','4π'])
plot_sine1(5, 3.4)
Explanation: Plotting with parameters
Write a plot_sin1(a, b) function that plots $sin(ax+b)$ over the interval $[0,4\pi]$.
Customize your visualization to make it effective and beautiful.
Customize the box, grid, spines and ticks to match the requirements of this data.
Use enough points along the x-axis to get a smooth plot.
For the x-axis tick locations use integer multiples of $\pi$.
For the x-axis tick labels use multiples of pi using LaTeX: $3\pi$.
End of explanation
interact(plot_sine1,a=(0.0,5.0,.1),b=(-5.0,5.0,.1));
assert True # leave this for grading the plot_sine1 exercise
Explanation: Then use interact to create a user interface for exploring your function:
a should be a floating point slider over the interval $[0.0,5.0]$ with steps of $0.1$.
b should be a floating point slider over the interval $[-5.0,5.0]$ with steps of $0.1$.
End of explanation
def plot_sine2(a,b,style):
    t = np.linspace(0,4*np.pi,400)
    plt.plot(t,np.sin(a*t + b),style)
    plt.xlim(0,4*np.pi)
    plt.ylim(-1.0,1.0)
    plt.xticks([0,np.pi,2*np.pi,3*np.pi,4*np.pi], ['0','π','2π','3π','4π'])
plot_sine2(4.0, -1.0, 'r--')
Explanation: In matplotlib, the line style and color can be set with a third argument to plot. Examples of this argument:
dashed red: r--
blue circles: bo
dotted black: k.
Write a plot_sine2(a, b, style) function that has a third style argument that allows you to set the line style of the plot. The style should default to a blue line.
End of explanation
interact(plot_sine2, a=(0.0,5.0,.1), b=(-5.0,5.0,.1), style={'Dotted Blue': 'b:', 'Black Circles': 'ko', 'Red Triangles':'r^'});
assert True # leave this for grading the plot_sine2 exercise
Explanation: Use interact to create a UI for plot_sine2.
Use a slider for a and b as above.
Use a drop down menu for selecting the line style between a dotted blue line line, black circles and red triangles.
End of explanation
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