How to Write the Equation of a Sine Graph
The general equation of a sine graph is \(y = a sin(b(x – h)) + k\), where \(a\) is the amplitude, \(b\) is the period, \(h\) is the horizontal shift, and \(k\) is the vertical shift.
Related Topics
- How to Graph the Sine Function
- How to Graph the Cosine Function
- How to Graph Inverse of the Sine Function
- How to Graph Inverse of the Cosine Function
Step-by-step to write the equation of a sine graph
To find out how to write the equation of a sine graph, follow the step-by-step guide below:
- Amplitude: The amplitude is the distance from the maximum or minimum value of the function to the midline (average of the maximum and minimum values). It is represented by the variable \(“a”\) in the equation.
- Period: The period is the distance between consecutive maximum or minimum values of the function. The period of the sine function is \(2π\). It is represented by the variable \(“b”\) in the equation.
- Horizontal Shift: The horizontal shift is the movement of the graph horizontally. It is represented by the variable \(“h”\) in the equation.
- Vertical Shift: The vertical shift is the movement of the graph vertically. It is represented by the variable \(“k”\) in the equation.
For example, if you want to write the equation of a sine graph with an amplitude of \(2\), a period of \(4π\), a horizontal shift of \(3\) units to the right and a vertical shift of \(1\) unit up, the equation would be \(y = 2 sin(\frac{(x – 3)}{(4π)} ) + 1\)
You can also use a graphing calculator or a software like Desmos to help you graph the function and find the equation.
It’s important to note that sine and cosine functions have an amplitude between \(-1\) and \(1\) and a period of \(2×pi\), and that the domain of these functions is all the real numbers.
Related to This Article
More math articles
- A Comprehensive Collection of Free TSI Math Practice Tests
- Best Office Chairs for Online Math Teachers
- Algebra Puzzle – Critical Thinking 12
- How to Prepare for Math Exams: Study Tips & Tricks
- Substitution Rule of Integrals: Integral Problems Made Simple
- The Ultimate Accuplacer Math Course (+FREE Worksheets)
- How to Prepare for the DAT Quantitative Reasoning Math Test?
- Number Properties Puzzle -Critical Thinking 1
- How to Factor the Difference between Two Perfect Squares?
- How to Add Mixed Numbers? (+FREE Worksheet!)
What people say about "How to Write the Equation of a Sine Graph - Effortless Math: We Help Students Learn to LOVE Mathematics"?
No one replied yet.