Understanding the Period of y 32sinx - 1

In this article, we will delve into the concept of the period of a sinusoidal function, focusing specifically on the function y 32sinx - 1. We will explore the general form of a sine function, how to identify and use its parameters, and ultimately determine the period of this particular function.

The General Form of a Sine Function

The general form of a sine function is given by:

y A BsinCx - D

Where:

A represents the vertical shift. B represents the amplitude. C affects the period. D represents the horizontal shift.

Identifying Parameters in the Given Function

Let's consider the specific function given:

y 3 2sinx 1

From this function, we can identify:

A 3 (vertical shift) B 2 (amplitude) C 1 (since the function can be rewritten as 32sin(1x - -1)) D 0 (no horizontal shift)

Calculating the Period

The period P of a sine function is given by the formula:

P 2pi / C

Applying this formula to our function:

P 2pi / 1 2pi

Thus, the period of the function y 3 2sinx 1 is 2pi.

General Sinusoidal Function and Period

Let's consider the general form of a sinusoidal function:

y alpha betasingamma x delta

The only factor determining the period of this function is gamma.

The period of a function with parameters as described above is:

P 2pi / gamma

In the case of the function 32sinx - 1, we can verify the period as follows:

y 32sinx - 1 can be rewritten as:

y 32sin(x * 1 - -1)

Here, gamma 1, so the period is: