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The paper investigates two types of real trigonometric polynomial equations: \[ A(\theta)y'=B_1(\theta)+B_n(\theta)y^n \] and \[ A(\theta)y^{n-1}y'=B_1(\theta)+B_n(\theta)y^n \] The authors focus on the first equation and demonstrate that when $n\geq 4$, it has a maximum of 3 real trigonometric polynomial solutions if $n$ is even and 5 real ...
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Solutions of Problems: Trigonometric and Inverse Trigonometric Functions
2021In this chapter, the problems of the 11th chapter are fully solved, in detail, step-by-step, and with different methods.
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Two trigonometric function solutions of the mKdV equations
Applied Mathematics Letters, 2023zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Da-jun Zhang, Feilong Zhang
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Trigonometric solutions of triangle equations. Simple lie superalgebras
Theoretical and Mathematical Physics, 1987See the review in Zbl 0648.58017.
Bazhanov, V. V., Shadrikov, A. G.
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Solution of Dual Trigonometrical Series Using Orthogonality Relations
SIAM Journal on Applied Mathematics, 1970Abstract : The unknown coefficients in dual trigonometrical series are found by a method which eliminates the need for assuming initially the forms of the expressions for the coefficients, and also for differentiating the original series term by term.
Noble, B., Whiteman, J. R.
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Trigonometric equations and their solution
1984It is often useful to express a cos θ + b sin θ as a single term such as r cos (θ − γ), where r is positive. This is possible if we can find r and y such that $$\begin{gathered} r\cos \left( {\theta -\gamma } \right)\equiv r\left( {\cos \theta \cos \gamma +\sin \theta \sin \gamma } \right) \hfill \\ \quad \quad \quad \quad \;\;\;\equiv a\cos \theta
J. E. Hebborn, C. Plumpton
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