Big Idea:

Big Idea 4

Trigonometric functions are characterized by the period and amplitude.

1 week

Evidence of Understanding

  • interpret the features of a trig function from its graph, table, or equation
    • graph f(x) = sinx and g(x) = cosx and describe the relationship between inputs and outputs
      • given any input, use the graph to identify the output
    • identify the period, amplitude, midline, and frequency for any trig function
    • explain connections between the unit circle and sine, cosine, and tangent functions
      • describe restrictions on the domain and range
      • identify intervals that are increasing, decreasing, positive, and negative
    • represent trigonometric functions in multiple formats, including graphically, in table form, and as a function rule
       
  • describe trig functions in relation to its parent function, f(x) = sinx, cosx, or tanx
    • given the parent graph and another trig graph, describe how a transformation on the parent function impacts the function’s amplitude, midline, period and/or frequency  
    • create a graph, table of values, or equation for a function from a stated transformation
    • write the function rule from the graph
    • possible extension: explore parent functions of f(x) = cscx, secx, or cotx and create a graph, table of values, or equation for a function from a stated transformation
       
  • use trigonometric functions to model different contexts
    • solve a real-world situation by creating and using a trigonometric function rule, graph, or table
      • analyze values to justify a trigonometric function model (and not linear, quadratic, or exponential)
    • interpret solutions using trigonometric function models
      • accept and reject possible solutions based on the context of the situation and the limitations on  reasonable domain and range values

Develop conceptual understanding:

frequency

Supporting terms to communicate:

function, input, output, domain, range, angle, cosine, sine, tangent, unit circle, reference angle, period, amplitude, midline, undefined, asymptote, interval, parent function, transformation
Core Resource
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    Instructional Routine: Contemplate then Calculate
    These tasks are embedded within the instructional routine called Contemplate then Calculate. COMING SOON!