Graphing y = sin(x) from 0 to 4π

Trigonometry · Axiom Academy

EXAMPLE Graphing y = sin(x) from 0 to 4π Learn to plot the sine function step-by-step using key points and predict the wave pattern. Excellent work! You've successfully graphed y = sin(x) from 0 to 4π. Here's what we learned: Key Points: The sine function has critical values at multiples of π/2: (0, 0), (π/2, 1), (π, 0), (3π/2, -1), (2π, 0) Periodic Pattern: The sine function repeats every 2π units. This is called the period of the function. Range: The y-values of sin(x) oscillate between -1 and 1, making the amplitude equal to 1. Smooth Curve: Between key points, sine creates a smooth, continuous wave pattern—never sharp corners or breaks. Starting and Ending: The function starts at (0, 0) and after two complete cycles returns to the same height at (4π, 0). Understanding this pattern is fundamental to trigonometry! You can now predict the behavior of sin(x) for any value and recognize its characteristic wave shape in applications ranging from sound waves to circular motion.

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