Solving a general complex trigonometric equation

In summary, to solve a general complex trigonometric equation, you can use various techniques such as substitution, factoring, and trigonometric identities. Some common trigonometric identities used in solving complex equations include the Pythagorean identities, sum and difference identities, double angle identities, and half angle identities. Complex equations can have multiple solutions due to the periodic nature of trigonometric functions, but it is important to specify the range of the solutions. When solving complex equations, imaginary numbers should be treated like any other variable and can be simplified using properties of complex numbers. There is no specific order to follow when solving complex trigonometric equations, but a good understanding of identities and techniques is necessary, along with careful simplification and checking
  • #1
omertech
13
0
Hello everyone!

Homework Statement


Solving a relatively general equation representing a constant combination of 2 trigonometric functions.

Homework Equations


[tex]a\cos{(vx+p)}+b\cos{(ux+q)}=c[/tex]

The Attempt at a Solution


I really don't have any idea for a general solution to this equation..

Best Regards
 
Last edited:
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  • #2
Not aware of any general analytic solution. Do you have a reason for believing such exists?
 

FAQ: Solving a general complex trigonometric equation

How do you solve a general complex trigonometric equation?

To solve a general complex trigonometric equation, you can use various techniques such as substitution, factoring, and trigonometric identities. The key is to simplify the equation and isolate the variable on one side of the equation.

What are some common trigonometric identities used in solving complex equations?

Some common trigonometric identities used in solving complex equations include the Pythagorean identities, sum and difference identities, double angle identities, and half angle identities.

Can complex equations have multiple solutions?

Yes, complex equations can have multiple solutions. This is because trigonometric functions are periodic and have infinite solutions. However, when solving a complex equation, you should specify the range of the solutions.

How do you handle imaginary numbers when solving complex equations?

When solving complex equations, imaginary numbers should be treated as any other variable. You can use the properties of complex numbers, such as the distributive property and the conjugate property, to simplify the equations and eliminate the imaginary numbers.

Is there a specific order to follow when solving complex trigonometric equations?

There is no specific order to follow when solving complex trigonometric equations. However, it is important to have a good understanding of trigonometric identities and techniques, and to carefully simplify the equations and check for extraneous solutions.

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