what is a sinusoidal function A sinusoidal function is a function in sine or in cosine The amplitude of a graph is the distance on the y axis between the normal line and the maximum minimum It is given by parameter a in function y asinb x c d or y acosb x c d The period of a graph is the distance on the x axis before the function repeats itself
Explanation Frequency is the number of occurrences of a repeating event per unit of time It is also referred to as temporal frequency which emphasizes the contrast to spatial frequency and angular frequency The period is the duration of time of one cycle in a repeating event so the period is the reciprocal of the frequency Let f be a generalized sinusoidal function whose graph is a sine wave f x Asin Bx C D Where A Amplitude 2pi B Period C B Phase shift D Vertical shift The maximum domain of a function is given by all the values in which it is well defined Domain x x in RR and f x is defined Since the sine function is defined everywhere on
what is a sinusoidal function
what is a sinusoidal function
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Y 4sin 2 x pi 2 6 The standard form of a sine function is y asin b x h k where a is the amplitude 2pi b is the period h is the phase shift and k is the vertical displacement We start with classic y sinx graph y sin x x 2 y 2 0 075 0 15 15 11 5 The circle at 0 0 is for a point of reference The amplitude of this function is a 1 To make the amplitude 4 we Use a sine function to describe the height of the tides of the ocean if high tide raises the water level to 5 metres at noon and low tide drops it down to 1 metre at 4 p m Let t 0 be 12 noon Trigonometry
Sinusoidal means a movement that goes in one direction then gradually slows down stops and changes into an opposite direction then again slows down stops and changes into an original direction This cycle repeats itself Presented on the time line X axis with directions of movement along the Y axis this behavior resembles the graph of a trigonometric A sinusoidal function is a function in sine or in cosine The amplitude of a graph is the distance on the y axis between the normal line and the maximum minimum It is given by parameter a in function y asinb x c d or y acosb x c d The period of a graph is the distance on the x axis before the function repeats itself
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1 Answer In a sinusoidal model of the form y a sin b x c d the period is found by taking 2 b Frequency is the reciprocal of period Example y 2 sin 3x would have a period of 2 3 which is one third the length of the normal period of 2 Another way to describe this change from the Parent function would be to If you have Asin omega x phi then A is the amplitude 2pi omega is the period phi is the shift The most general case of a sine function is Asin omega x phi Let s see what they do Since the sine function is bounded between 1 and 1 if we multiply the function by A the result will be bounded between A and A So the amplitude is decided by the outter
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what is a sinusoidal function - A sinusoidal function is a function in sine or in cosine The amplitude of a graph is the distance on the y axis between the normal line and the maximum minimum It is given by parameter a in function y asinb x c d or y acosb x c d The period of a graph is the distance on the x axis before the function repeats itself