# What exactly does the period tell you in a trig graph?

• mathkillsme
In summary, the period of a trigonometric function indicates the length of one complete cycle of the function and helps determine its behavior and properties.

## Homework Statement

i understand how to find the period of a trig equation... (either 2pi/|b| for sin and cos or pi/|b| for tan etc. but i do not understand what information the period tells me..

## Homework Equations

alright for example.. if my problem is y= 4sin2x

## The Attempt at a Solution

the period in the above solution would be pi... correct? so what does that tell me?

If you graph it, you will find that 4sin(2x) repeats itself after every multiple of pi. To be precise, the period of a function f(x) is the smallest number T such, for all x, f(x) = f(x + T). In this case, you will notice that pi is the smallest number such that, for all x, 4sin(2x) = 4sin(2(x + pi)) = 4sin(2x + 2pi).

## 1. What is the purpose of the period in a trigonometric graph?

The period in a trigonometric graph represents the length of one complete cycle of the function. It helps to identify the frequency at which the function repeats itself and can also be used to determine the amplitude and phase shift of the graph.

## 2. How do you calculate the period of a trigonometric function?

The period of a trigonometric function can be calculated by finding the distance between two consecutive peaks or valleys on the graph. It is equal to 2π divided by the coefficient of x in the function's equation.

## 3. Can the period of a trigonometric function be negative?

No, the period of a trigonometric function cannot be negative. It represents a distance or a time, which cannot have a negative value.

## 4. What happens to the period when the coefficient of x is changed in a trigonometric function?

The period of a trigonometric function is inversely proportional to the coefficient of x. This means that as the coefficient increases, the period decreases and vice versa. Changing the coefficient also affects the frequency and amplitude of the graph.

## 5. How does the period affect the shape of a trigonometric graph?

The period of a trigonometric function determines the length of one cycle and therefore, affects the shape of the graph. A longer period results in a stretched out graph, while a shorter period leads to a compressed graph. The period also determines the number of peaks and valleys in the graph.