What is the purpose of the trigonometric equation AsinX + BcosX = Ksin(X+a)?

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The equation AsinX + BcosX = Ksin(X+a) serves to simplify trigonometric expressions, often transforming them into a more manageable form. The values A, B, and K represent coefficients that influence the amplitude and phase of the resulting sine function. This equation can also be expressed as Kcos(X-a), providing flexibility in solving trigonometric problems. Its primary application lies in simplifying equations like AcosX + BsinX = constant. Understanding this equation enhances problem-solving efficiency in trigonometry.
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Hello All,

I have been given a assignment to find out information regarding the following Equation;

'AsinX + BcosX = Ksin(X+a)'

I need some help finding out where this forula is used as well as what the A,B and K values do in the equation.

Looking forward to hearing about the equation,

Thanks
 
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Endorser said:
Hello All,

I have been given a assignment to find out information regarding the following Equation;

'AsinX + BcosX = Ksin(X+a)'

I need some help finding out where this forula is used as well as what the A,B and K values do in the equation.

It is just another way to write it in the compound angle form. It could also be written in the form Kcos(X-a) as well.

It is sometimes beneficial to have an equation in a contracted form as 'Ksin(X+a)' since it will be easier to solve a given equation.
 
rock.freak667 said:
It is just another way to write it in the compound angle form. It could also be written in the form Kcos(X-a) as well.

but what is the purpose of the equation and where do we use it??
 
Endorser said:
but what is the purpose of the equation and where do we use it??

There is no set purpose per se, like I said, it is used to simplify equations such as Acosx+Bsinx=0.25.
 
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