Math CentralQuandaries & Queries


Question from Cheryl, a student:

Find all solutions of the following equation and show how to do this algebraically.
4cos^2 (3x) + 3sin (3x) = 1


I can help get you started.

Use the fact that sin2(A) + cos2(A) = 1 to rewrite the equation in the form f(x) =0 where f(x) is an expression with a sin2(3x) term a sin(3x) term and a constant term. Let y = sin(3x) and then this becomes a quadratic equation. Solve the equation for y and then find x from y = sin(3x).


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