PRECAL.MATH.4.A

Determine the relationship between the unit circle and the definition of a periodic function to evaluate trigonometric functions in mathematical and real-world problems.

Precalculus · Texas Essential Knowledge and Skills (TEKS) · TEKS 2012

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Vocabulary
unit circleperiodic functiondefinitiontrigonometric functionsmathematical problemsreal-world problemsrelationshipevaluation
Skills
  • determine (relationship between the unit circle and the definition of a periodic function) #dok2
  • evaluate (trigonometric functions using the unit circle) #dok2
  • apply (understanding of the unit circle and periodic functions in mathematical problems) #dok3
  • apply (understanding of the unit circle and periodic functions in real-world problems) #dok3
Learning Targets
  • I can identify the unit circle and its components. #dok1
  • I can recognize the properties of periodic functions. #dok1
  • I can explain the connection between the unit circle and periodic functions. #dok2
  • I can determine the value of trigonometric functions using the unit circle. #dok2
  • I can use the unit circle to evaluate trigonometric functions in mathematical and real-world problems. #dok3
  • I can model periodic real-world phenomena using trigonometric functions based on the unit circle. #dok3
Big Ideas
  • The unit circle provides a foundation for understanding and evaluating trigonometric functions.
  • Trigonometric functions model periodic behavior in both mathematical contexts and real-world situations.
Essential Questions
  • How does the unit circle define the values of trigonometric functions?
  • What does it mean for a function to be periodic and how is that property shown on the unit circle?
  • How can the unit circle be used to evaluate trigonometric functions in real-life contexts?
  • How are mathematical problems involving periodicity modeled using trigonometric functions and the unit circle?
  • Why is an understanding of the unit circle essential to evaluating trigonometric functions?