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.

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.

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.

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.

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.