Understanding Sine and Cosine Functions Periodicity in Mathematics

periodic property of sin and cosine

because the period of the sin/cos function is 2pi, you can add 2pi to sin(-value) to make it positive

The sine and cosine functions are periodic functions. This means that their values repeat in a regular pattern after a certain interval of input values. The period of a sine or cosine function is the smallest value of x for which the function repeats.

For the sine function, its period is 2π. This means that the value of sin(x) at x = 0 is the same as sin(x) at x = 2π, sin(x) at x = 4π, sin(x) at x = 6π, and so on. Similarly, sin(x) at x = π is the same as sin(x) at x = 3π, sin(x) at x = 5π, sin(x) at x = 7π, and so on. In general, sin(x) repeats its values after every 2π interval.

For the cosine function, its period is also 2π. So, cos(x) at x = 0 is the same as cos(x) at x = 2π, cos(x) at x = 4π, cos(x) at x = 6π, and so on. Additionally, cos(x) at x = π/2 is the same as cos(x) at x = 5π/2, cos(x) at x = 9π/2, cos(x) at x = 13π/2, and so on. In general, cos(x) repeats its values after every 2π interval.

Knowing the period of a periodic function is important in understanding its properties and behavior. It allows us to predict the values of the function at different points and to identify patterns and relationships between different parts of the function.

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