A playground has a sinusoid ramp. A brick curb starts 0.75 ft above the ground and slopes up to 3.25 ft above the ground, 44 ft away. The concrete walkway varies from 0.75 ft below this curb to 0.25 ft below it, see picture in attachment. Let x be the number of feet from the beginning of the ramp.
Write a equation of g(x), the distance from the ground to the top of the concrete walkway. Take into account the slope of the ramp.
I know the slope of the brick curb is y2-y1/x2-x1=3.25-0.75/44-0=2.5/44
Sinusoid formula: y=A cos B(x-D) + C
B = 2?/Period = 2?/8 = ?/4
A (amplitude) = 1/2(0.75-0.25) = 0.25 ft
According to the answer sheet, the sinusoidal axis is at y=0.25 when x=0 and goes up with slope 2.5/44. The sinusoid is at a low point when x=0 so the phase displacement is 0.
The answer for g(x) = 0.25 + (2.5/44)x - 0.25 cos (?/4)x
Need help on the following:
1) I thought the sinusoidal axis is the line that passes thru the middle of the sin curve. If that is true, the midpoint should be 1/2(.75+.25)=.5 but it's 0.25 (according to the answer). Why???
2) Why is displacement 0?
3) Why is the sign negative in front of cos?
Write a equation of g(x), the distance from the ground to the top of the concrete walkway. Take into account the slope of the ramp.
I know the slope of the brick curb is y2-y1/x2-x1=3.25-0.75/44-0=2.5/44
Sinusoid formula: y=A cos B(x-D) + C
B = 2?/Period = 2?/8 = ?/4
A (amplitude) = 1/2(0.75-0.25) = 0.25 ft
According to the answer sheet, the sinusoidal axis is at y=0.25 when x=0 and goes up with slope 2.5/44. The sinusoid is at a low point when x=0 so the phase displacement is 0.
The answer for g(x) = 0.25 + (2.5/44)x - 0.25 cos (?/4)x
Need help on the following:
1) I thought the sinusoidal axis is the line that passes thru the middle of the sin curve. If that is true, the midpoint should be 1/2(.75+.25)=.5 but it's 0.25 (according to the answer). Why???
2) Why is displacement 0?
3) Why is the sign negative in front of cos?