You are watching: A sound wave is modeled with the equation y=1/4 cos 2pi/3
Click here to see ALL troubles on Trigonometry-basicsQuestion 1013983: 12. A sound tide is modeled through the equation y = 1/4 cos 2pi/3 θ. A. Discover the period. Describe your method. B. Uncover the amplitude. Define your method.I need help with this! thank you...
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(Show Source): You deserve to put this equipment on her website! the an easy formula for cosine is:y = a * (b * (x-c)) + da is the amplitude.b is the frequency.c is the horizontal displacement.d is the upright displacement.your equation is y = 1/4 * cos (2*pi/3 * x).i provided x instead of theta.no matter.just replace my x with your theta and also you have your answer.the amplitude is 1/4.the frequency is 2 * pi/3.the horizontal displacement is 0.the vertical displacement is 0.if you room dealing in degrees, then the period is same to 360 divided by the frequency.if you space dealing in radians, then the duration is equal to 2*pi separated by the frequency.if you understand the frequency, you have the right to solve for the duration using this formula.if you know the period, you can solve for the frequency making use of this formula.consider f = frequency and also p = periodin degrees:p = 360 / fsolve because that f to acquire f = 360 / pen radians: ns = 2pi / fsolve because that f to acquire f = 2pi / psince you"re in radians, we"ll use the radian formula come get:p = 2pi/(2pi/3)this is the exact same as ns = 2pi * 3 / 2pithe an outcome is that p = 3.if girlfriend graph this equation, her x-axis will certainly be in radians and also one complete cycle the the cosine wave will certainly take up 3 radians.here"s the graph of her equation.the normal period is 2pi in radians.the equation that y = cos(x) is yes, really y = cos(1*x).1 is the frequency.p = 2pi/f becomes p = 2pi/1 which becomes p = 2pi.when the frequency is 1, the duration is 2pi.the adhering to graph that y = cos(x) mirrors that:in both cases, the cosine to be starts at 1 and ends in ~ 1.that"s because cos(0) = 1 and cos(360) = 1in radians, cos(0) = 1 and also cos(2pi) = 1also, cos(180) = -1 and also cos(pi) = -1when the period is 2pi, halfway v the duration is pi.when the duration is 3, halfway v the period is 1.5.convert 3 radians come degrees and you acquire 3 radians * 180 / pi = 171.8873385 degrees.half of the is equal to 75.84355826 degrees.convert the to radians and also you acquire 75.84355826 levels * pi / 180 = .4774648293 * pi radians which is same to 1.5 radians.