Understanding the Behavior of sin(2x) | Period, Critical Points, and Maximum/Minimum Points

sin(2x)

The function sin(2x) is a trigonometric function that represents the sine of twice the angle x

The function sin(2x) is a trigonometric function that represents the sine of twice the angle x. In other words, it is the sine function applied to the double of the input angle.

To understand its behavior, let’s discuss some important properties of the function sin(x). The sine function is periodic with a period of 2π, which means it repeats its values every 2π units. It oscillates between the values of -1 and 1, and it has several key points known as critical points. The critical points occur at x = 0, π, 2π, etc., where the value of sin(x) is zero. Additionally, the function has maximum and minimum points at x = π/2, 3π/2, 5π/2, etc., where the value of sin(x) is respectively 1 and -1.

Now, when we consider sin(2x), it means we are doubling the angle x before applying the sine function. This has an effect on the period and critical points. Since we are multiplying x by 2, the period of sin(2x) becomes π, which means it repeats its values every π units. The critical points occur at x = 0, π/2, π, 3π/2, 2π, etc., where the value of sin(2x) is zero. The maximum and minimum points occur at x = π/4, 3π/4, 5π/4, etc., where the value of sin(2x) is respectively 1 and -1.

In summary, sin(2x) is a function that doubles the angle x before taking the sine value. It has a period of π, critical points at x = 0, π/2, π, 3π/2, etc., and maximum and minimum points at x = π/4, 3π/4, 5π/4, etc.

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