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Learning Goal

Part of: Model periodic phenomena with trigonometric functions2 of 3 cluster items

Restrict domain for inverse trig functions

HSF.TF.B.6

**HSF.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.

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HSF.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.

What you'll learn

  1. Explain why sine, cosine, and tangent are not one-to-one on their full domains and therefore do not have inverses without restriction
  2. Identify the standard restricted domains: sin on [-pi/2, pi/2], cos on [0, pi], tan on (-pi/2, pi/2)
  3. Justify why each restricted domain produces a one-to-one function (always increasing or always decreasing)
  4. State the domain and range of arcsin, arccos, and arctan
  5. Evaluate inverse trigonometric functions at standard values (e.g., arcsin(1/2) = pi/6)
  6. Explain why the restricted domain choice is a convention and recognize that other restrictions would produce different inverse functions

Slides

Interactive presentations perfect for visual learners • Interactive presentation

Slide Video

Watch narrated slides play like a video lesson • Narrated slide playback

Exercises

Practice problems to build fluency and understanding • 1 exercises