what is the amplitude of the sinusoids graph y 4sin3x Answer Amplitude 4 Step by step explanation The general form of a sine curve would be where A is the amplitude or the tallness or shortness of the graph Technically amplitude is the absolute value of the number that is multiplied in front of Sin So the amplitude is 4
1 Answer Alan P Aug 5 2015 Amplitude of 4sin 3x is 4 Period of 4sin 3x is 6 Explanation y sin has an amplitude of 1 XXXXy varies between 1 and 1 If y 4sin XXXX then y will vary between 4 and 4 XXXX y 4sin has an amplitude of 4 for any y k sin has a period of 2 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 Example y 2 sin x
what is the amplitude of the sinusoids graph y 4sin3x
what is the amplitude of the sinusoids graph y 4sin3x
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Trigonometry Find Amplitude Period and Phase Shift y 4sin 3x y 4sin 3x y 4 sin 3 x Use the form asin bx c d a sin b x c d to find the variables used to find the amplitude period phase shift and vertical shift a 4 a 4 b 3 b 3 c 0 c 0 d 0 d 0 Find the amplitude a a Amplitude 4 4 You might need Calculator Below is the graph of a trigonometric function It intersects its midline at 2 3 1 2 and it has a minimum point at 4 3 3 4 1 2 3 4 5 6 7 8 9 2 3 4 1 2 3 4 5 6 7 8 9 2 3 4 y x 2 3 1 2 4
The amplitude is the vertical distance from the midline to the min or max So if you are given the minimum add the amplitude to the y coordinate If you are given the maximum subtract the amplitude from the y coordinate The graphing window shows two sinusoids A reference sinusoid in cyan and a transformed sinusoid in yellow The reference sinusoid is the graph of y t cos omega t That is it has amplitude 1 and phase lag 0 The transformed sinusoid is f t A cos omega t phi
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Range 1 y 1 Period 2 the pattern of the graph repeats in intervals of 2 Amplitude 1 the sine graph is centered at the x axis 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 Since the phase shift is dfrac pi 8 and this is a sine function the coordinates of P are dfrac pi 8 2 Since the period is dfrac pi 2 the t coordinate of R is dfrac pi 8 dfrac 1 2 dfrac pi 2 dfrac 3 pi 8 So
Answer link It is one half of the difference between the maximum and minimum values of y Example y 7sin 3x 2 4 has a maximum of 11 and a minimum of 3 The amplitude is 1 2 11 3 1 2 14 7 Note that the amplitude is the absolute value of the coefficient of sin 3x 2 Explore math with our beautiful free online graphing calculator Graph functions plot points visualize algebraic equations add sliders animate graphs and more
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what is the amplitude of the sinusoids graph y 4sin3x - Amplitude A 2 period 2 B 2 4 2 phase shift 0 5 or 0 5 to the right vertical shift D 3 In words the 2 tells us it will be 2 times taller than usual so Amplitude 2 the usual period is 2 but in our case that is sped up made shorter by the 4 in 4x so Period 2 and the 0 5 means it will be shifted