Equations in Trigonometry

Solving Trigonometric Equations

  • Understand the approaches for solving simple trigonometric equations for radians and degrees within a given domain.
  • Be equipped to solve equations involving multiple angles, such as sin(2x) or cos(3x).
  • Get comfortable with the methodology used for solving equations involving trigonometric identities, with emphasis on exact value solutions.
  • Appreciate that the solution of such equations may yield extraneous roots which fall outside the prescribed domain.

Manipulation of Trigonometric Equations

  • Develop adeptness in the manipulation of trigonometric equations involving sums and differences of angles.
  • Be familiar with the process of transforming an equation by use of double, half-angle or angle sum and difference formulas.
  • Be able to apply these transformation techniques in order to find solutions to trigonometric equations, or simplify the equations themselves.
  • Master the art of factorising or expanding trigonometric expressions where appropriate.

Trigonometric Solutions in Real World Modelling

  • Apply the principles of solving trigonometric equations in the context of real-world modelling problems, such as wave function, harmonic motions or periodic phenomena like sound or light waves.
  • Be familiar with the notation used in such contexts, and be able to sketch and interpret trigonometric functions representing these models.

Graphical Understanding of Trigonometric Equations

  • Learn to associate solutions of trigonometric equations with geometric properties, such as intersections of a circle with a line.
  • Relate the root finding problem in trigonometric equations to the corresponding situation on the graph of y = sinx, y = cosx or y = tanx.
  • Understand the role the unit circle plays in solving trigonometric equations, and be able to find solutions using this method.