How to find the equation of a sine graph
What is the equation of a sine graph?
An investigation of y = a sin (bx+c) for different values of a, b, and c. The graphs of functions defined by y = sin x are called sine waves or sinusoidal waves. Notice that the graph repeats itself as it moves along the x-axis.
How do you find the equation of a graph?
To write an equation in slope-intercept form, given a graph of that equation, pick two points on the line and use them to find the slope. This is the value of m in the equation. Next, find the coordinates of the y-intercept–this should be of the form (0, b). The y- coordinate is the value of b in the equation.
How do you find B in a sine graph?
To get the period of the sine curve for any coefficient b, just divide 2π by the coefficient b to get the new period of the curve. The coefficient b and the period of the sine curve have an inverse relationship, so as b gets smaller, the length of one cycle of the curve gets bigger.
How does a sine graph look like?
To graph the sine function, we mark the angle along the horizontal x axis, and for each angle, we put the sine of that angle on the vertical y-axis. The result, as seen above, is a smooth curve that varies from +1 to -1. Curves that follow this shape are called ‘sinusoidal’ after the name of the sine function.
How do you graph the equation of a line?
To graph a linear equation, we can use the slope and y-intercept.Locate the y-intercept on the graph and plot the point.From this point, use the slope to find a second point and plot it.Draw the line that connects the two points.
How do you find the equation of a graph given two points?
Equation from 2 points using Slope Intercept FormCalculate the slope from 2 points.Substitute either point into the equation. You can use either (3,7) or (5,11)Solve for b, which is the y-intercept of the line.Substitute b, -1, into the equation from step 2.
What is the formula of a function?
A function is an equation that has only one answer for y for every x. A function assigns exactly one output to each input of a specified type. It is common to name a function either f(x) or g(x) instead of y. f(2) means that we should find the value of our function when x equals 2.
How do you graph a cosine equation?
How to Graph a Cosine FunctionFind the values for domain and range. Like with sine graphs, the domain of cosine is all real numbers, and its range is.Calculate the graph’s x-intercepts. Calculate the graph’s maximum and minimum points. Sketch the graph of the function.
What is the period of a graph?
Any one full pattern in the graph is called a cycle, and the length of an interval over which a cycle occurs is called the period. The period is equal to the value .
How do you tell if a graph is sine or cosine?
Look at the graphs of the sine and cosine functions on the same coordinate axes, as shown in the following figure. The graph of the cosine is the darker curve; note how it’s shifted to the left of the sine curve. The graphs of y = sin x and y = cos x on the same axes.
What is the formula for phase shift?
The phase shift equation is ps = 360 * td / p, where ps is the phase shift in degrees, td is the time difference between waves and p is the wave period. Continuing the example, 360 * -0.001 / 0.01 gives a phase shift of -36 degrees.