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UTPA STEM/CBI Courses/Calculus/Inverse Trigonometric Functions (Feng)

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Backwards Design

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Course Objectives

  • Primary Objectives- By the next class period students will be able to:
    • Understand the inverse sine, inverse cosine, and inverse tangent functions.
    • Evaluate inverse trigonometric functions for some special angles such as pi/6, pi/4 and pi/3 and related angles.
    • Evaluate an expression with mixed trigonometric functions and inverse trigonometric functions.
  • Sub Objectives- The objectives will require that students be able to:
    • Undertand the definition of trigonometric functions
    • Understand what is the inverse funciton
    • At what domain the Sine, Cosin and Tangent are one-to-one functions
  • Difficulties- Students may have difficulty:
    • Confused with the notation of trig. functions and inverse trig. functions
    • Distinguish the difference between them
  • Real-World Contexts- There are many ways that students can use this material in the real-world, such as:
    • periodic motion, estimate the height of the building.

Model of Knowledge

  • Concept Map
    • Inverse Function
    • Definition of trigonometric functions
    • Definition of inverse trigonometric functions
  • Content Priorities
    • Enduring Understanding
      • Inverse sine, inverse cosine, inverse tangent functions.
      • Evaluate inverse trigonometric functions for some classical numbers.
      • Use the calculator to evaluate inverse trigonometric functions for arbitrary numbers.
    • Important to Do and Know
      • Know the domain and range for each inverse trigonometric function.
      • Inverse trigonometric function identities.
    • Worth Being Familiar with
      • Composing a trigonometric function and an inverse.
      • Graphs of inverse trigonometric functions and their relationship with the graphs of trigonometric functions.

Assessment of Learning

  • Formative Assessment
    • In Class (groups)
      • none
    • Homework (individual)
      • from textbook
      • online homework on webassign
  • Summative Assessment
    • weekly quiz
    • exam

Legacy Cycle

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OBJECTIVE

By the next class period, students will be able to:

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The objectives will require that students be able to:

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THE CHALLENGE

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GENERATE IDEAS

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MULTIPLE PERSPECTIVES

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RESEARCH & REVISE

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TEST YOUR METTLE

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GO PUBLIC

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Pre-Lesson Quiz

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Various material can be tested here, depending on time constraints.

Test Your Mettle Quiz

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Various material can be tested here, depending on time constraints.