Exploring the Graph of Sin(x) | Understanding the Fundamental Trigonometric Function’s Periodicity and Symmetry

Graph of sin(x)

The graph of sin(x), also known as the sine function, is a fundamental trigonometric function that represents the relationship between the angle (x) and the y-coordinate of a point on the unit circle

The graph of sin(x), also known as the sine function, is a fundamental trigonometric function that represents the relationship between the angle (x) and the y-coordinate of a point on the unit circle.

The sine function is periodic, meaning that it repeats itself after a certain interval. In the case of the sine function, the period is 2π radians or 360 degrees. This means that for any angle x, we can find an equivalent angle x + 2πk, where k is an integer, that yields the same sine value.

The graph of sin(x) starts at the origin (0,0) and extends infinitely in both positive and negative directions. As x increases from 0 to 2π (or from 0 to 360 degrees), the y-coordinate of the corresponding points on the sine graph oscillates between 1 and -1.

At x = 0, sin(0) = 0, which is why the graph starts at the origin. As x increases, the graph moves upward, reaching a maximum value of 1 at x = π/2 (or 90 degrees). From there, the graph starts descending until it reaches the x-axis (y = 0) again at x = π (or 180 degrees).

Continuing further, the graph dips below the x-axis, reaching its minimum value of -1 at x = 3π/2 (or 270 degrees). Finally, the graph rises again and intersects the x-axis at x = 2π (or 360 degrees), completing one full period and starting the cycle again.

It is important to note that the graph of sin(x) has symmetry about the origin. This means that if you reflect the portion of the graph for x > 0 across the y-axis, you will get the graph for x < 0. Overall, the sin(x) graph is a smooth, wavy curve that repeats its pattern indefinitely in a sinusoidal fashion. It is commonly used in many fields such as physics, engineering, and mathematics to model various periodic phenomena.

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