Equations - Trigonometric Inequation Cotan

Trigonometric Inequation – Cotangent

Definition and Solution Interval

A trigonometric inequation involving cotangent compares \( \cot x \) to a constant \( m \). The solution set is derived based on the cotangent function's periodicity and principal value range from \( 0 \) to \( \pi \).

Graphical explanation of cotangent inequation

Key Inequation

\[ \cot x \geq m \]

The solution interval for real values of \( m \) is:

\[ k\pi \leq x \leq \alpha + k\pi \]

where \( \alpha = \text{arccot } m \), and \( 0 \leq \alpha \leq \pi \).

Applications

  • Used in solving advanced trigonometric inequalities.
  • Applicable in engineering fields involving periodic signals and phase angles.
  • Helpful in evaluating angular constraints in modeling scenarios.
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