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scientifico
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Homework Statement
sen(2x) * sen(x) = sen(4x) * sen(3x)
The Attempt at a Solution
I applied product to sum and sum to product identities and now I get cos(3x)=cos(7x ) how can I solve it?
thank you
scientifico said:I applied product to sum and sum to product identities and now I get cos(3x)=cos(7x)
What is this?tiny-tim said:so 3x = ±7x + … ?
To solve a goniometric equation, you need to use the properties and identities of trigonometric functions, such as the sum and difference formulas, double angle formulas, and half angle formulas. You also need to manipulate the equation using algebraic techniques to isolate the variable.
The steps to solve this specific goniometric equation are:
Yes, the double angle formula for sine, sum and difference formulas for sine, and double angle formula for cosine are all useful in solving this equation. Additionally, the solutions involve the special angles of 0, pi/2, and pi/6, which can be used to simplify the equation.
Yes, this equation can have multiple solutions, as shown in the steps above. The solutions will depend on the values of k, which can result in an infinite number of solutions.
You can check if a solution is correct by substituting it back into the original equation and simplifying both sides. If the resulting expressions are equal, then the solution is correct. You can also use a calculator or graphing software to plot the equations and see if they intersect at the given solution.