Mathematics, Calculus, Trigonometry
Material Type:
Ohio Open Ed Collaborative
  • Amplitude
  • Cosine
  • Mathematics
  • Period
  • Periodic Function
  • Phase Shift
  • Sine
  • Sinusoidal Function
  • Tmm0022
  • Trigonometric Function
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    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)

    1. Functions:

    • 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).*

    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.

    Learning Objectives:

    • 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
    • Sinusoids
    • 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