how to find amplitude of a function

Asked by: Payton Jacobson

Updated: 5 April 2020 01:02:00 AM

How to find the amplitude of a trig function?

The amplitude of y=asin(x) and y=acos(x) represents half the distance between the maximum and minimum values of the function.

Consequently, where is the amplitude in a trig function?

The amplitude of a trigonometric function is half the distance from the highest point of the curve to the bottom point of the curve: (Amplitude) = (Maximum) - (minimum) 2 .

Аdditionally how do you find the amplitude of a function?

Amplitude is the distance between the center line of the function and the top or bottom of the function, and the period is the distance between two peaks of the graph, or the distance it takes for the entire graph to repeat. Using this equation: Amplitude =APeriod =2πBHorizontal shift to the left =CVertical shift =D.

In the same vein what is amplitude in trig?

The amplitude of a function is the amount by which the graph of the function travels above and below its midline. When graphing a sine function, the value of the amplitude is equivalent to the value of the coefficient of the sine. The amplitude is dictated by the coefficient of the trigonometric function.

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Related questions and answers

Where does a sine graph start?

Let's use a cosine function because it starts at the highest or lowest value, while a sine function starts at the middle value. A standard cosine starts at the highest value, and this graph starts at the lowest value, so we need to incorporate a vertical reflection.

What is b sine graph?

The value B is the number of cycles the graph completes in an interval of from 0 to 2π or 360º. The value B affects the period. The period of sine and cosine is. . When 0 < B < 1, the period of the function will be greater than 2π and the graph will be a horizontal stretching.

How do you stretch a sine graph?

To stretch a graph vertically, place a coefficient in front of the function. This coefficient is the amplitude of the function. For example, the amplitude of y = f (x) = sin(x) is one. The amplitude of y = f (x) = 3 sin(x) is three.

How do you tell the difference between sine and cosine graphs?

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 the frequency of a sine wave?

The frequency of a sine wave is the number of complete cycles that happen every second. (A cycle is the same as the period, see below.) In the bouncing weight above, the frequency is about one cycle per second.

How do you find the frequency of a graph?

Determining wave frequency from a graph

Determining wave frequency from a graph.
f • Frequency = #of cycles/time • Measured in Hertz (Hz)
• 1 cycle = 1 full wave to repeat itself.
31 2 4 5 6 7 8 9 10 11 12 Time in seconds 3 cycles.
from 0 to 12 seconds 31 2 4 5 6 7 8 9 10 11 12 Time in seconds 0.
f=3 /12 s = ¼ Hz 31 2 4 5 6 7 8 9 10 11 12 Time in seconds.

How does amplitude change a graph?

The sinusoidal axis and amplitude of a trig function graph. By multiplying a trigonometry function by certain values, you can make the graph taller or shorter: Positive values of amplitudes greater than 1 make the height of the graph taller. you multiply the height of the original sine graph by 2 at every point.

What 3 digits are in the thousands period?

Notice that the digits 3, 0, and 2, are in the thousands period. This represents "three hundred two thousand". In the ones period are the digits 0, 2, and 0, which represent twenty. To the right of the decimal point are the digits 0, 2, 0, and 1.

How does b affect a sine graph?

The change in variable b has affected the frequency of the sine graph and has increased it by the product of the value of b. For b = -2, we get the equation y = sin(-2x), which is overlayed on the graph in comparison to the original y = sin(x) graph.

What is a period in 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.

Does a sine graph always start at 0?

The Sine Function has this beautiful up-down curve (which repeats every 2π radians, or 360°). It starts at 0, heads up to 1 by π/2 radians (90°) and then heads down to −1.

What is a period math?

more In Mathematics: The length from one peak to the next (or from any point to the next matching point) of a periodic function. In other words the length of one full cycle.

What is the period?

Menstruation, or period, is normal vaginal bleeding that occurs as part of a woman's monthly cycle. Every month, your body prepares for pregnancy. If no pregnancy occurs, the uterus, or womb, sheds its lining. The menstrual blood is partly blood and partly tissue from inside the uterus.

What does a cos graph look like?

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. It is the same shape as the cosine function but displaced to the left 90°.

What is the period of a graph?

The period is the length of the smallest interval that contains exactly one copy of the repeating pattern. So the period of or is . Any part of the graph that shows this pattern over one period is called a cycle. For example, the graph of on the interval is one cycle.

How do you find the period and amplitude of a sine function?

To write a sine function you simply need to use the following equation: f(x) = asin(bx + c) + d, where a is the amplitude, b is the period (you can find the period by dividing the absolute value b by 2pi; in your case, I believe the frequency and period are the same), c is the phase shift (or the shift along the x-axis

Is phase shift always positive?

phase shift can be affected by both shifting right/left and horizontal stretch/shrink. Phase shift is positive (for a shift to the right) or negative (for a shift to the left). The easiest way to find phase shift is to determine the new 'starting point' for the curve.

What does a sine curve 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.

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).

How does amplitude affect a graph?

When 0 < a < 1, the amplitude of the graph decreases, causing the slopes of the graph to appear more "flat". When a > 1, the amplitude of the graph increases, causing the slopes of the graph to appear more "steep". This shows that changing the a affects the amplitude of the graph.

What is the equation for a sine graph?

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.