The period of a periodic function is the interval of x-values on which one copy of the repeated pattern occurs . Notice that in the graph of the sine function shown that f(x) = sin(x) has period 2π, because the graph from x = 0 to x = 2π repeats itself forever in both directions.
How do you find the period of a sine graph?
The period of the sine curve is the length of one cycle of the curve. The natural period of the sine curve is 2π. So, a coefficient of b=1 is equivalent to a period of 2π. 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.
What is the period of a graph?
The period is defined as the length of one wave of the function . In this case, one full wave is 180 degrees or radians. You can figure this out without looking at a graph by dividing with the frequency, which in this case, is 2.
What is a period in sine function?
The period of a trigonometry function is the extent of input values it takes for the function to run through all the possible values and start all over again in the same place to repeat the process. In the case of the function y = sin x, the period is 2π , or 360 degrees.
What is a period in sin and cos graphs?
Periodic functions repeat after a given value. The smallest such value is the period. The basic sine and cosine functions have a period of 2π . The function sin x is odd, so its graph is symmetric about the origin. The function cos x is even, so its graph is symmetric about the y-axis.
What is the period wave?
Wave Period: The time it takes for two successive crests (one wavelength) to pass a specified point . The wave period is often referenced in seconds, e.g. one wave every 6 seconds.
What 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 tell if a graph is cosine or sine?
In a cosine graph, a positive or negative number vertically flips the graph and determines whether the graph starts at the maximum (if it’s positive) or minimum (if it’s negative). For a sine graph, a positive or negative number vertically flips the graph like it does with a cosine graph.
What is cosine period?
The cosine function is a trigonometric function that’s called periodic. ... The period of a periodic function is the interval of x-values on which the cycle of the graph that’s repeated in both directions lies. Therefore, in the case of the basic cosine function, f(x) = cos(x), the period is 2π .
Is period and frequency the same?
Frequency and period are distinctly different, yet related, quantities. Frequency refers to how often something happens . Period refers to the time it takes something to happen. Frequency is a rate quantity.
Why is the period 2pi B?
It means the period is 12, so each cycle is 12 units long. What you say is sort of right: b is the number of cycles per 2pi .
Can an amplitude be negative?
The amplitude or peak amplitude of a wave or vibration is a measure of deviation from its central value. Amplitudes are always positive numbers (for example: 3.5, 1, 120) and are never negative (for example: -3.5, -1, -120).
What is cosine graph?
To graph the cosine function, we mark the angle along the horizontal x axis , and for each angle, we put the cosine of that angle on the vertical y-axis. The result, as seen above, is a smooth curve that varies from +1 to -1. ... As you do so, the point on the graph moves to correspond with the angle and its cosine.
