# How can i tell a period of a function involving sin and cos

• th3plan
In summary, the period of a function involving sin and cos is the length of one complete cycle of the function, which can be determined by finding the distance between two consecutive peaks or troughs. The period can also be calculated without graphing by looking at the coefficient inside the sin or cos function. The period and frequency of a function are inversely related, and the amplitude of a function does not affect its period. The period cannot be negative and can be represented by its absolute value if necessary.
th3plan

## Homework Statement

Ok so we started Fourier Analysis in circuits. How can i tell the Period of a function that's let's say sin(2t)+3cos(5t) something like that . Any help or url's that have information on this

For your example, the period of sin(2t) is pi and the period of cos(5t) is 0.4pi. The smallest interval that is a multiple of both pi and 0.4 pi is 2pi, so that would be the period of the sum of the two functions.

## 1. How do I determine the period of a function involving sin and cos?

The period of a function involving sin and cos is the length of one complete cycle of the function. This can be determined by finding the distance between two consecutive peaks or troughs of the function. This distance is also known as the wavelength.

## 2. Can I determine the period of a function without graphing it?

Yes, you can determine the period of a function without graphing it by looking at the coefficient of the variable inside the sin or cos function. The period is equal to 2π divided by the coefficient. For example, if the function is sin(3x), the period is 2π/3.

## 3. What is the relationship between the period of a function and its frequency?

The period and frequency of a function are inversely related. This means that as the period increases, the frequency decreases, and vice versa. The frequency is equal to 1 divided by the period.

## 4. Can the period of a function be negative?

No, the period of a function cannot be negative. The period is a measure of distance and, therefore, cannot have a negative value. If you are working with a negative period, it may be helpful to use its absolute value instead.

## 5. How does the amplitude of a function affect its period?

The amplitude of a function does not affect its period. The period is solely determined by the coefficient inside the sin or cos function. The amplitude only affects the height of the peaks and troughs of the function.

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