Restrict domain for inverse trig functions

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Lesson Plan →Objectives, pacing and practice, built from this lesson's brief.
Guided Notes →One page your students fill in and keep.
Exit Ticket →Three items at the end of class. No student accounts.
Re-teach →After an exit ticket: who missed what, and what to do tomorrow.
Homework →Assign practice; it grades itself.

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.

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

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

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Restrict domain for inverse trig

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