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Mathematics > Course Model Precalculus (Advanced Course) > Trigonometric Functions
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Mathematics | Course : Model Precalculus (Advanced Course)

Domain - Trigonometric Functions

Cluster - Model periodic phenomena with trigonometric functions.

[PC.F-TF.B.6] - (+) Understand that restricting a trigonometric function to a domain on which it is always increasing or always decreasing allows its inverse to be constructed.

Resources:


  • Inverse function
    A function obtained by expressing the dependent variable of one function as the independent variable of another; that is the inverse of y = f(x) is x = f –1(y).
  • Trigonometric function
    A function (as the sine, cosine, tangent, cotangent, secant, or cosecant) of an arc or angle most simply expressed in terms of the ratios of pairs of sides of a right-angled triangle.

Predecessor Standards:

No Predecessor Standards found.

Successor Standards:

No Successor Standards found.

Same Level Standards:

  • AI.F-BF.B.4
    Find inverse functions algebraically and graphically.
  • AI.F-BF.B.4.a
    Solve an equation of the form f(x) = c for a linear function f that has an inverse and write an expression for the inverse.
  • AII.F-IF.B.4
    For a function that models a relationship between two quantities, interpret key features of graphs and tables in terms of the quantities, and sketch graphs showing key features given a verbal description of the relationship. Key features include: intercepts; intervals where the function is increasing, decreasing, positive, or negative; relative maximums and minimums; symmetries; end behavior; and periodicity.*
  • AII.F-IF.C.7.e
    Graph exponential and logarithmic functions, showing intercepts and end behavior; and trigonometric functions, showing period, midline, and amplitude.*
  • MII.F-BF.B.4
    Find inverse functions algebraically and graphically.
  • MII.F-BF.B.4.a
    Solve an equation of the form f(x) = c for a linear function f that has an inverse and write an expression for the inverse.
  • MIII.F-IF.B.4
    For a function that models a relationship between two quantities, interpret key features of graphs and tables in terms of the quantities, and sketch graphs showing key features given a verbal description of the relationship. Key features include: intercepts; intervals where the function is increasing, decreasing, positive, or negative; relative maximums and minimums; symmetries; end behavior; and periodicity.*
  • MIII.F-IF.C.7.e
    Graph exponential and logarithmic functions, showing intercepts and end behavior, and trigonometric functions, showing period, midline, and amplitude.*
  • PC.F-BF.B.4
    Find inverse functions.
  • PC.F-BF.B.4.b
    (+) Verify by composition that one function is the inverse of another.
  • PC.F-BF.B.4.c
    (+) Read values of an inverse function from a graph or a table, given that the function has an inverse.
  • PC.F-BF.B.4.d
    (+) Produce an invertible function from a non-invertible function by restricting the domain.
  • PC.F-TF.A.4
    (+) Use the unit circle to explain symmetry (odd and even) and periodicity of trigonometric functions.
  • PC.F-TF.B.7
    (+) Use inverse functions to solve trigonometric equations that arise in modeling contexts; evaluate the solutions using technology, and interpret them in terms of the context.*
  • AQR.F-TF.A.4
    (+) Use the unit circle to explain symmetry (odd and even) and periodicity of trigonometric functions.
  • AQR.F-TF.B.7
    (+) Use inverse functions to solve trigonometric equations that arise in modeling contexts; evaluate the solutions using technology, and interpret them in terms of the context.*