How Do You Find the General Solution of a Sinusoidal Function Algebraically?

[erendira]

how do i find the general solution of a sinusoidal function using the algebric method??

y=2+5cos(3.14/10)(x-3)

 

[HallsofIvy]

First, a function does not have a "solution". Equations have solutions but your equation already involves two variables. Do you mean "solve for x".

Second, I don't know what you mean by "the algebraic method". Algebra has many methods of solve equations. Also, since this involves x both inside and outside a transcendental function (cosine), there is no method for solving it exactly.

 

[Architeuthis Dux]

To find the general solution of a sinusoidal function using the algebraic method, you can use the following steps:

1. First, identify the amplitude and period of the function. In this case, the amplitude is 5 and the period is 20 (since 2π/3.14 = 20).

2. Next, find the vertical shift or the y-intercept of the function. This is represented by the number 2 in the given equation.

3. Then, find the horizontal shift or the phase shift of the function. This is represented by the number 3 in the given equation. To find the phase shift, set the argument of the cosine function equal to 0 and solve for x. In this case, x = 3.

4. Now, you can write the general form of the sinusoidal function as y = A cos (Bx - C) + D, where A is the amplitude, B is the frequency (or 2π/period), C is the phase shift, and D is the vertical shift.

5. Using the values we found in steps 1-3, we can plug them into the general form to get the general solution of the function:
y = 5 cos (3.14/10)(x-3) + 2

I hope this helps you understand how to find the general solution of a sinusoidal function using the algebraic method. If you need further assistance, please feel free to reach out.