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Learning Trigonometry Using Python

Objective

To understand sine and cosine functions visually using Python by plotting their graphs, using a slider to change the angle, and observing automatic movement of points representing sin(θ) and cos(θ).

Tools Used

  • Python 3.12\
  • NumPy (mathematical calculations)\
  • Matplotlib (graph plotting and slider interaction)

How the Program Works

1. Angle Generation

Angles from 0° to 360° are generated and converted into radians because Python's trigonometric functions work with radians.

2. Calculating sin and cos values

Using NumPy, sine and cosine values are calculated for all angles. These values form fixed curves.

3. Plotting the Graphs

The sine and cosine curves are plotted on the graph. These curves remain constant.

4. Moving Dots

Dots are placed on the curves to represent the values of sin(θ) and cos(θ) for the selected angle.

5. Slider Interaction

A slider is used to change the angle dynamically. When the slider moves, the angle changes automatically.

6. Automatic Update

When the angle changes, the program recalculates sin(θ) and cos(θ) and moves the dots accordingly.

Issues Faced and Solutions

Issue 1: Matplotlib not installed

Reason: Required library was missing.
Solution: Installed using pip.

Issue 2: Graph not changing

Reason: Expected graph to move.
Solution: Learned that graphs stay fixed and only dots move.

Issue 3: Dot not moving

Reason: Canvas was not refreshing automatically.
Solution: Used fig.canvas.draw_idle().

Issue 4: Runtime Error -- x must be a sequence

Reason: Matplotlib requires data as lists.
Solution: Passed values inside lists.

Final Working Python Code

import numpy as np
import matplotlib.pyplot as plt
from matplotlib.widgets import Slider

x_deg = np.linspace(0, 360, 1000)
x_rad = np.radians(x_deg)

y_sin = np.sin(x_rad)
y_cos = np.cos(x_rad)

fig, ax = plt.subplots(figsize=(8, 5))
plt.subplots_adjust(bottom=0.25)

ax.plot(x_deg, y_sin, label="sin x")
ax.plot(x_deg, y_cos, label="cos x")

ax.set_xlim(0, 360)
ax.set_ylim(-1.1, 1.1)
ax.set_xticks(np.arange(0, 361, 30))
ax.set_yticks(np.arange(-1, 1.1, 0.2))
ax.grid(True)

sin_dot, = ax.plot([0], [0], 'go', markersize=10)
cos_dot, = ax.plot([0], [1], 'ro', markersize=10)

ax.set_xlabel("Angle (degrees)")
ax.set_ylabel("Value")
ax.legend()

slider_ax = plt.axes([0.15, 0.1, 0.7, 0.05])
angle_slider = Slider(slider_ax, "Angle (°)", 0, 360, valinit=0)

def update(angle):
    rad = np.radians(angle)
    sin_dot.set_data([angle], [np.sin(rad)])
    cos_dot.set_data([angle], [np.cos(rad)])
    fig.canvas.draw_idle()

angle_slider.on_changed(update)

plt.show()

Conclusion

This project demonstrates how Python can be used to understand trigonometric concepts visually. It makes learning interactive, reduces memorization, and improves conceptual clarity.