Answer:
1) Amplitude; A = 80 ft
Period = 60 ft
2)y = 80 sin ((π/30)x - 5π) + 80
3)y = 40 sin ((π/30)x - 5π) + 80
4)y = 40 sin ((π/30)x - 5π) + 40
5)y = -65sin ((π/30)x - 5π) + 80
Step-by-step explanation:
The general formula for sinusoidal wave equation is given by;
y = A sin (Bx - C) + D
Where;
A is amplitude = D_max or D_min
Period = 2π/B
So; B = 2π/Period
Phase Shift = C/B
So; C = B · Phase Shift
D: center
We are Given:
Height of the field is 160 ft and so the center is at y = 80. Thus; D = 80 ft
Thus; A = 80 ft
The person closest to Darla on the same horizontal line, stands 10 yards(30 ft) Thus, period = 2 × 30 = 60 ft
Thus; B = 2π/60 = π/30
Field is 300 ft wide and so the center is 300/2 = 150 ft
Thus; Phase Shift = 150.
C = B × Phase Shift = π/30 · 150 = 5π
1) From the calculations above,
Amplitude; A = 80 ft
Period = 60 ft
2) As they begin to play, from the calculations above and y = A sin (Bx - C) + D, equation of the sine function is now;
y = 80 sin ((π/30)x - 5π) + 80
3) In this, since the sine wave is half as tall, then after the changes, we have;
y = 40 sin ((π/30)x - 5π) + 80
4) since they have moved closer, then equation is now;
y = 40 sin ((π/30)x - 5π) + 40
5) We are Given:
Height of the field is 160 ft and so the center is at y = 80. Thus; D = 80 ft
Since the first person forming the curve now stands at the 5 yard line, the minimum is at 5 yds (15 ft). Thus;
D_min = 80 - 15 = 65. Thus; A = 65 ft
The person closest to Darla on the same horizontal line, stands 10 yards(30 ft) Thus, period = 2 × 30 = 60 ft
Thus; B = 2π/60 = π/30
Field is 300 ft wide and so the center is 300/2 = 150 ft
Thus; Phase Shift = 150.
C = B × Phase Shift = π/30 · 150 = 5π
The band ends down (at 15 feet) and thus A is negative
The equation is;
y = -65sin ((π/30)x - 5π) + 80
