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

No Core Resource for this Big Idea.

Consider using the Instructional Routines linked below for teaching towards this Big Idea.