Period in Decimals and Periodic Functions Explained
What is a Period?
Have you ever wondered how long you have to wait before the lunch bell rings or your next birthday arrives? This time is known as the ‘period’ in maths. We all have attended classes where there are separate periods for different subjects to be taught, right?
How do you think the whole day is divided into these periods? This is done by calculating the time that a teacher needs to dedicate to a class every day in order to teach a subject properly to the students. Let us learn more about periods in this article.
Definition of Period in Mathematics
In mathematics, the time interval or gap between two given points is known as a period. This period can be as little as a few microseconds. For instance, the time gap or period between today and tomorrow is one day. There can be variations in the amount or span of time that makes up a period.
In Physics and Maths, the period is generally calculated in terms of time or distance. However, in this article, we will concentrate on the time factor in calculating periods.
Examples of Time Periods
The following are a few examples of standard periods with respect to time. Learn the given examples thoroughly as these will help you throughout your life to count time periods for general cases.
Second - A second can be defined in maths or physics as the time taken by one caesium-133 atom to complete 9192631770 full oscillations (oscillation means the to and fro movement of an object within a given space). Events like track races, blinking of eyes, and so on are generally timed using seconds.
Minute - A minute is equal to 60 seconds. A minute is more time than a second, and this unit of the period is generally used in cases like short car rides, workouts, and so on.
Hour - An hour is equal to 60 minutes. Hours are usually used to time longer periods, for instance, cricket matches, surgeries, and so on.
Day - A day comprises 24 hours. A day is usually the complete cycle of a person’s regular schedule. Starting from waking up in the morning, doing all the work, eating, resting, and so on, till the time a person wakes up again the next morning, is considered one day. The Earth completes one rotation around its axis in 1 day.
Month - A month has 30 days on average, while some months have 31 days. February has 28 days (in a leap year, which comes every four years, February has 29 days). Months are longer periods of time that are generally used for calculating salary, rent, subscriptions, and so on.
Year - A year consists of 12 months and it is a huge period of time where a lot can happen. Your birthday comes every year. The Earth completes one revolution around the Sun every year.
Conclusion
A period, in Maths, is generally measured in time and it is primarily known as the time taken to reach one point to another. Periods can even exceed years. For instance, a decade comprises 10 years and a century has 100 years in it.
The term period has a lot of different definitions, but in maths, the concept of the period is very important to deal with problems related to time. Hence, it is advisable that you learn this concept properly and try to memorise as many units and measures of standard periods as possible.
FAQs on What Is Period in Maths with Simple Explanation
1. What is period in maths?
The period in maths is the smallest positive value for which a function or pattern repeats itself. In other words, it is the length of one complete cycle in a repeating pattern or periodic function.
- In trigonometry, it tells how long a graph takes to repeat.
- In decimal numbers, it refers to repeating digits.
- In place value, it can mean a group of digits separated by commas.
2. What is the period of a function?
The period of a function is the smallest positive number T such that f(x + T) = f(x) for all x in the domain. This means the function repeats its values after every T units.
- If f(x + T) = f(x), then T is the period.
- The smallest such T is called the fundamental period.
- Example: For sin x, the period is 2π.
3. What is the period of sin x and cos x?
The period of both sin x and cos x is 2π (or 360°). This means their graphs repeat after every 2π radians.
- sin(x + 2π) = sin x
- cos(x + 2π) = cos x
- In degrees, the period is 360°.
4. How do you find the period of a trigonometric function?
The period of a trigonometric function of the form sin(Bx) or cos(Bx) is given by 2π / |B|. The value of B changes how quickly the graph repeats.
- For sin(Bx) or cos(Bx): Period = 2π / |B|
- For tan(Bx): Period = π / |B|
- Example: For sin(3x), Period = 2π/3.
5. What is the period of tan x?
The period of tan x is π (or 180°). This means the tangent function repeats its values every π radians.
- tan(x + π) = tan x
- In degrees, the period is 180°.
- For tan(Bx), Period = π / |B|.
6. What is a period in decimal numbers?
In decimal numbers, a period refers to the repeating part of a recurring decimal. It is the group of digits that repeats infinitely.
- Example: In 0.333..., the period is 3.
- In 0.142857142857..., the period is 142857.
- Such numbers are called recurring or repeating decimals.
7. What does period mean in place value?
In place value, a period is a group of three digits separated by commas in large numbers. Each period helps read and write numbers correctly.
- Example: In 4,567,891:
- 891 → Ones period
- 567 → Thousands period
- 4 → Millions period
8. What is the formula for the period of a wave?
The period of a wave is given by the formula T = 1 / f, where f is the frequency. It represents the time taken for one complete cycle.
- T = Period
- f = Frequency
- Example: If f = 5 Hz, then T = 1/5 = 0.2 seconds.
9. What is the difference between period and frequency?
The period is the time for one complete cycle, while frequency is the number of cycles per second. They are inversely related.
- Period (T) = time for one cycle
- Frequency (f) = number of cycles per second
- Relationship: T = 1/f and f = 1/T
10. Can you give an example of finding the period of a function?
To find the period of y = 4cos(2x), use the formula 2π / |B|, giving a period of π. Here B = 2.
- Given function: y = 4cos(2x)
- Formula: Period = 2π / |B|
- Calculation: 2π / 2 = π
- The coefficient 4 does not affect the period.
