sin function

[daberace]

Hi, I need help with graphing a sinusoidal graph.

What would be the equation of this situation? The formula is this y=a sin(k(x-d))+c. I calculated this but I dont think its right. y=5489 sin(4 x-40)+20
“The object was seen above Mount Saint Elias which is about 5489m high. It travelled in a wave like pattern as if it was searching for something.
It then made its way towards the earth where it dipped below the treeline of 40m.
It then re-appeared above the treeline and went back to its original position.
It repeated this pattern about 20 times before it flew off.
The whole incident took about 4 mins from start to finish.”

 

[skeeter]

[MATH]y = A\sin[K(t - D)]+C[/MATH] ... the sinusoidal motion is a function of time

period of motion is [MATH]\dfrac{4 \, min}{20} = 12 \, sec \implies K = \dfrac{2\pi}{12} = \dfrac{\pi}{6}[/math]
cannot say anything definite about amplitude ... above a mount of 5489 ft and below a tree line of 40 ft offers nothing definite to determine the maximum and minimum positions.
if one used those values as the maximum and minimum, then the value of A would not be 5489.

if the initial sighting was at maximum height, I’d go with using a cosine function to avoid having to deal with calculating a horizontal shift

 

[Steven G]

The highest point of a sine curve is NOT the amplitude. The amplitude is the average of the highest and lowest points. Is that information given?

 

[Harry_the_cat]

The highest point of a sine curve is NOT the amplitude. The amplitude is the average of the highest and lowest points. Is that information given?

No. The amplitude is half the distance between the highest value and the lowest value of the function.
The average of the highest and lowest values is the height where the equilibrium line is positioned.

 

[HallsofIvy]

There is NO "sin function". (It would be immoral if there were!)

There is the "sine function" which is written "sin(x)".

 

[Steven G]

No. The amplitude is half the distance between the highest value and the lowest value of the function.
The average of the highest and lowest values is the height where the equilibrium line is positioned.

You got me good!