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

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To find the general solution of a sinusoidal function algebraically, it's important to clarify that functions do not have solutions, but equations do. The equation provided, y=2+5cos(3.14/10)(x-3), involves two variables, which complicates the process. The term "algebraic method" is vague, as algebra encompasses various techniques for solving equations. Due to the presence of the cosine function, which is transcendental, there is no exact method for solving for x when it appears both inside and outside the function. Understanding these distinctions is crucial for approaching sinusoidal equations.
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how do i find the general solution of a sinusoidal function using the algebric method??

y=2+5cos(3.14/10)(x-3)
 
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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.
 

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