Consider the equation $\cos(kx) = a$, where $k$ and $a$ are real parameters with $k > 0$. Analyse the number of solutions for $x$ in the interval $[0, 2\pi]$ as both $k$ and $a$ vary. Specifically, discuss how the number of solutions changes depending on the values of $k$ and $a$, paying particular attention to the cases when $|a| > 1$ and when $k$ is a non-integer.
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Create Free Account Log inThis is a free VCE Units 3 & 4 Mathematical Methods practice question worth 7 marks, testing your understanding of Literal and General Equations. It falls under Algebra, number and structure in Unit 3: Mathematical Methods Unit 3. Submit your answer above to receive instant AI-powered marking and personalised feedback.
Extend introductory study of functions, algebra, calculus. Focus on functions, relations, graphs, algebra, and applications of derivatives.
Covers algebra of functions, inverse functions, and solutions of equations and systems of equations.
solution of literal equations and general solution of equations involving a single parameter
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