what is the amplitude of either a sine or cosine parent function Both the normal sine and cosine functions sway between 1 and 1 When you add a coefficient you are multiplying that positive one or negative one by the coefficient giving you a new amplitude equal to the absolute value of your coefficient
Given any function of the form y a sin b x or y a cos b x you know how to find the amplitude and period and how to use this information to graph the functions Given a graph of a sine or cosine function you also can determine the amplitude and period of The height from the horizontal axis to the peak or through of a sine or cosine function is called the amplitude of the function Each of the curves y sin y sin and y cos y cos has amplitude 1
what is the amplitude of either a sine or cosine parent function
what is the amplitude of either a sine or cosine parent function
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Transformations Of The Sine Function Changing The Amplitude And
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The Difference Between Amplitude And Frequency Sound Explained Rocky
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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 and d is the vertical Let b be a real number The period of y a sin b x and y a cos b x is given by Period 2 b Example Find the period and amplitude of y 5 2 cos x 4 Solution Compare the functions y 5 2 cos x 4 and y a cos b x to find a and b Amplitude a 5 2 5 2
The amplitude of the sinusoidal functions y A sin Bx C D and y A cos Bx C D is A the absolute value of the parameter A Figure PageIndex 12 Amplitude dfrac A A 2 A The amplitude of the sine and cosine functions is the vertical distance between the sinusoidal axis and the maximum or minimum value of the function In relation to sound waves amplitude is a measure of how loud something is What is the most common mistake made when graphing the amplitude of a sine wave
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Identifying the Amplitude of a Sine or Cosine Function What is the amplitude of the sinusoidal function f x 4 sin x f x 4 sin x Is the function stretched or compressed vertically The amplitude of a trigonometric function is half the distance from the highest point of the curve to the bottom point of the curve text Amplitude frac text Maximum minimum 2 Amplitude 2 Maximum minimum For example if we consider the graph of y sin x y sin x
The amplitude is the distance between the line around which the sine function is centered referred to here as the midline and one of its maxima or minima Zeros n the sine graph has zeros at every integer multiple of sin x sin x the graph of sine is odd meaning that it is symmetric about the origin The amplitude of a function is defined as the distance from the central axis to the maximum or minimum value of the function In the case of the sine and cosine functions the central axis is called the sinusoidal axis The amplitude can also be defined as half the distance between the maximum value and the minimum value of the function
Pre Calculus 40S Section C Fall 2015 Graphing Sine Functions
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what is the amplitude of either a sine or cosine parent function - Let b be a real number The period of y a sin b x and y a cos b x is given by Period 2 b Example Find the period and amplitude of y 5 2 cos x 4 Solution Compare the functions y 5 2 cos x 4 and y a cos b x to find a and b Amplitude a 5 2 5 2