1. A sine function has the following key features:Frequency = 16πAmplitude = 2Midline: y = 3y-intercept: (0, 3)The function is not a reflection of its parent function over the x-axis.Use the sine tool to graph the function. The first point must be on the midline and the second point must be a maximum or minimum value on the graph closest to the first point.2. A sine function has the following key features:Period = 12Amplitude = 4Midline: y = 1y-intercept: (0, 1)The function is not a reflection of its parent function over the x-axis.Use the sine tool to graph the function. The first point must be on the midline and the second point must be a maximum or minimum value on the graph closest to the first point.3. A sine function has the following key features:Period = 4πAmplitude = 2Midline: y = 3y-intercept: (0, 3)The function is a reflection of its parent function over the x-axis.Use the sine tool to graph the function. The first point must be on the midline and the second point must be a maximum or minimum value on the graph closest to the first point.4. picture 5. picture
Accepted Solution
A:
Problem 1
See the attached image (figure 1)
16pi seems like a typo. I'm going to assume that it's a fraction and it is 1/(6pi) f = 1/(6pi) = frequency T = 1/f = 1/(1/(6pi)) = 6pi Amplitude = 2 a = 2 b = 2pi/T = 2pi/(6pi) = 1/3 Midline: y = 3 d = 3
The function is y = a*sin(bx-c)+d y = 2*sin(1/3*x-0)+3 y = 2*sin(x/3)+3
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Problem 2
See the attached image (figure 2)
T = 12 is the period a = 4 is the amplitude b = 2pi/T = 2pi/12 = pi/6 y = 1 is the midline so d = 1 The y intercept is (0,1) which is the midline, which indicates no phase shifts have occurred so c = 0
The function is y = a*sin(bx-c)+d y = 4*sin((pi/6)x-0)+1 y = 4*sin((pi/6)x)+1
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Problem 3
See the attached image (figure 3)
Period = 4pi T = 4pi b = 2pi/T = 2pi/(4pi) = 1/2 = 0.5 Amplitude = 2 a = 2 Midline: y = 3 d = 3 y-intercept: (0,3) The function is a reflection of its parent function over the x-axis, so 'a' is negative meaning a = -2 instead of a = 2
The function is y = a*sin(bx-c)+d y = -2*sin(0.5x-0)+3 y = -2*sin(0.5x)+3
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Problem 4
See the attached image (figure 4)
a = 10 which is half of the distance between the highest and lowest points T = 8 is the period b = 2pi/T = 2pi/8 = pi/4 c = -pi/2 is the phase shift since its really a cosine graph d = 0 is the midline
The function is y = a*sin(bx-c)+d y = 10*sin((pi/4)*x+(-pi/2))+0 y = 10*sin((pi/4)*x+pi/2)
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Problem 5
See the attached image (figure 5)
a = 2 is the amplitude since it bobs up and down this distance from the midline T = 8 seconds is the period (double that of the time it takes for it to go from the highest to the lowest point) b = 2pi/T = 2pi/8 = pi/4 c = 0 is the phase shift as the buoy starts at normal depth of 20 meters d = 20 is the midline
The function is y = a*sin(bx-c)+d y = 2*sin((pi/4)x-0)+20 y = 2*sin((pi/4)x)+20