Chapter 10.5 - Exercises
Khan Academy - Graphing Sine Function
Khan Academy - Graphing Sinusoids
Graphs of Cosine and Sine Functions
Sine and Cosine Functions - amplitude, period, phase-shift, sinusoidal functions, periodic functions
TMM 002 PRECALCULUS (Revised March 21, 2017)
- 1a. Analyze functions. Routine analysis includes discussion of domain, range, zeros, general function behavior (increasing, decreasing, extrema, etc.), as well as periodic characteristics such as period, frequency, phase shift, and amplitude. In addition to performing rote processes, the student can articulate reasons for choosing a particular process, recognize function families and anticipate behavior, and explain the implementation of a process (e.g., why certain real numbers are excluded from the domain of a given function).*
Section 1: Graphs of Cosine and Sine Functions
As noted previously, circular functions can be treated as functions of real numbers. In this module we will graph the Cosine and Sine functions.
Review: Even-Odd property, coterminal angle property, domain and range of the Cosine and Sine functions.
- Periodicity and Periodic Functions; period of Cosine and Sine functions.
- Domain and Range of Cosine and Sine Functions
- Fundamental Cycle
- Apply transformations to find the graphs of f(x) = A COS (Bx + C) + D and A.SIN(BX + C) + D
- Amplitude, phase-shift, period and vertical-shift
- Rewrite sum or difference of cosine and/or
- sine expressions in terms of f(x) = A COS (Bx + C) + D or A.SIN(BX + C) + D