h t t p : / / w w w . j i s k h a . c o m / d i s p l a y . c g i ? i d = 1 2 6 0 2 2 5 7 6 7
ok this is what i mean. For exmaple take this problem that I asked for help with before
Naturalists find that the populations of some kinds of predatory animals vary periodically. Assume that the population of foxes in a certain forest varies sinusoidally with time. Records started being kept when t = 0 years. A minimum number, 200 foxes, occured when t = 2.9 years. The next maximum, 800 foxes, occurred at t = 5.1 years
use the formula I provided in other post
using points in problem that are max and min
max (A,B) = (5.1, 800)
A = 5.1
B = 800
Min = (C, D) = (2.9, 200)
plug and chug and you get the sinusodial funciton.
my question was how to rearange that formula for A, B, C, D, X, given all the other variables
you can just show me the formula if you want sense the work is probably a lot
I really need to know how to rearange the formula given all but X and the other formulas for A, B, c, D, or a second priority but is still something I need to know how to do but don't know how to
thanks
C = 2.9
D = 200
forgot to mention that put I implied that
No. Reread my post, that is the way to procede.
the amplitude is max-min divided by 2
The max occures at PI/2. Set all in the sine function to PI/2 at the max, That gives you one equaiton. Then, set all in the sine function equalto 3PI/2 for the min,and you should see enough equations to solve all those variable.
khalybalak
To rearrange the formula for A, B, C, D, and X in the sinusoidal function, consider the following steps:
1. Start with the general form of the sinusoidal function:
y = A * sin(B * (x - C)) + D
2. Substitute the given values for the maximum and minimum points:
For the maximum point: (5.1, 800)
Substitute A = 800 and C = 5.1:
800 = A * sin(B * (5.1 - C)) + D
For the minimum point: (2.9, 200)
Substitute A = -200 (negative because it's a minimum) and C = 2.9:
200 = -200 * sin(B * (2.9 - C)) + D
3. Rearrange equations to isolate A, B, D, and X:
-200 * sin(B * (2.9 - C)) + D = 200
Divide both sides by -200 and simplify:
sin(B * (2.9 - C)) - D/200 = -1
800 = A * sin(B * (5.1 - C)) + D
Divide both sides by A and simplify:
sin(B * (5.1 - C)) = (800 - D)/A
Now you have two equations with two unknowns (B and (5.1 - C)). Solve them simultaneously using algebraic techniques or numerical methods to find B and (5.1 - C).
4. Once you have B and (5.1 - C), you can substitute them back into either equation to find the values of A and D.
5. Finally, rearrange the formula to solve for X:
x - C = arcsin((y - D)/A) / B
x = arcsin((y - D)/A) / B + C
Remember, these steps provide a general approach to rearranging the given formula for A, B, C, D, and X based on the given conditions.