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

Backwards Design

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

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

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

Test Your Mettle Quiz

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