sine cosine functions amplitude 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 theta and y cos theta has amplitude 1
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 Amplitude and Period of Sine and Cosine Functions The amplitude of y a sin x and y a cos x represents half the distance between the maximum and minimum values of the function Amplitude a 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
sine cosine functions amplitude
sine cosine functions amplitude
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Transforming Sin Cos Graphs Graphing Sin And Cosine Functions
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How do you write an equation for a cosine function with an amplitude of 2 3 a period of pi and a vertical shift of 2 units up How do you find the amplitude and period of a function y sin 2pi x 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
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 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
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Sine Cosine and Tangent The main functions in trigonometry are Sine Cosine and Tangent They are simply one side of a right angled triangle divided by another For any angle Sine Cosine and Tangent are often abbreviated to sin cos and tan Amplitude and Period In other lessons you have dealt with how find the amplitude of a wave or the period of a wave Here we ll take a few minutes to work problems that involve both the amplitude and period giving us two variables to work with when thinking about sinusoidal equations
Find a formula for a sinusoidal function that has an amplitude of 3 a period of 24 and is shifted 2 units to the right and 4 units upwards compared with the cosine function Sketch the graph for 0 leq x leq 24 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
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sine cosine functions amplitude - How do you write an equation for a cosine function with an amplitude of 2 3 a period of pi and a vertical shift of 2 units up How do you find the amplitude and period of a function y sin 2pi x