Trig. Functions

Trig. Functions

Trigonometric Functions

Definitions and Basic Concepts

  • Gain a strong understanding of trigonometric functions including, but not limited to, sine (sin), cosine (cos), tangent (tan), cosecant (csc), secant (sec), and cotangent (cot).
  • Learn to identify and create periodic functions, which are functions that repeat their values in regular intervals.
  • Develop an appreciation for the relationship between radians and degrees, and understand how to convert between the two.

Trigonometric Identities

  • Learn to recognise and apply more complex trigonometric identities, such as the product-to-sum and sum-to-product identities.
  • Understand how to use the cofunction identities (sin(π/2 - θ) = cos θ), etc., to enable simplification of expressions and solutions to problems.

Inverse Trigonometric Functions

  • Familiarise yourself with the concept of inverse trigonometric functions (sin⁻¹, cos⁻¹, tan⁻¹ etc.) and their respective domains and ranges.
  • Apply your knowledge of these inverse functions to solve complex problems and evaluate unknown quantities.
  • Understand the relationship between a function and its inverse, especially focusing on the sin x function and its inverse.

Graphs of Trigonometric Functions

  • Understand how trigonometric functions can be transformed, and how these transformations can affect their graphs.
  • Issues to consider include amplitude, period, phase shift, as well as horizontal and vertical transformations.
  • Draw and interpret graphs of csc, sec, and cot, in addition to sin, cos, and tan. Identify behaviours such as asymptotes and points of inflection.
  • Recognise the impact of domain restrictions on the graph of inverse trigonometric functions.

Solving Trigonometric Problems

  • Master techniques to solve more complex trigonometric problems, such as those involving multiple angles or periodic functions.
  • Use your understanding of inverse trigonometric functions to solve equations, and your knowledge of identities to simplify expressions and prove equivalences.
  • Understand and apply the principle of the compound angle formula to break down more complex problems into simpler ones.