Reflection: Rigor Inverse Trig Functions - Day 1 of 2 - Section 2: Explore

 

It is easy to forget that trigonometry stems from simple right triangles, and the abstraction gets even more intense when we start working with inverse functions. In order for students to complete this very rigorous work, they must use a understanding of the regular trigonometric functions, inverses, and transformations.

As some students were working on the y = arccot(x) graph, I heard them talk about how the asymptotes were really helpful to sketch the function. Since they knew that x = 0 and x = pi are asymptotes of y = cot(x), then they knew that y = 0 and y = pi must be asymptotes of the inverse function since the inputs and outputs switch places. Also, many students were thinking of the graphical meaning of an inverse (a reflection over the line y = x) to help them sketch the new function.

  Rigor: Using Asymptotes
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Inverse Trig Functions - Day 1 of 2

Unit 4: Trigonometric Functions
Lesson 8 of 14

Objective: SWBAT restrict the domains of the trig functions in order to produce an inverse.

Big Idea: Use a graphical perspective to establish inverse trig functions.

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