3.1

Topic

Periodic Phenomena

Practice by unit: Trigonometric and Polar Functions

Sub-standards

• 3.1.A.1 — Construct graphs of periodic relationships based on verbal representations. A periodic relationship can be identified between two aspects of a context if, as the input values increase, the output values demonstrate a repeating pattern over successive equal-length intervals.
• 3.1.A.2 — The graph of a periodic relationship can be constructed from the graph of a single cycle of the relationship.
• 3.1.B.1 — Describe key characteristics of a periodic function based on a verbal representation. The period of the function is the smallest positive value k such that f x( + k) = f (x) for all x in the domain. Consequently, the behavior of a periodic function is completely determined by any interval of width k.
• 3.1.B.2 — The period can be estimated by investigating successive equal-length output values and finding where the pattern begins to repeat.