# Inverse Trigonometric Functions

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## Objective

SWBAT find the angles for any trig function given the measurements of the lengths or the ratio.

#### Big Idea

How can we find an angle measure without a protractor? Take a lesson from the Greeks and use inverse trigonometric functions!

## Set the Stage

5 minutes

I begin class by reading some of the examples students gave in the previous lesson (No Angle Left Behind) or by giving examples of real-life applications of trig functions.  I make sure to finish with the Hydrogen Atom example from the Trig Example Problems resource.  I then ask students to consider individually what methods they would use to solve that problem.  (MP1, MP2, MP4)  I allow a few minutes for thinking then have students share their ideas with a partner.  I ask each student to explain his/her plan, then to critique each other’s plan (MP3).  I invite students to share with the class and allow brief discussion about which plan would be the easiest, best, etc.  This helps build student confidence for working with trig functions.  I then read the Refraction Example and ask students to follow the same procedure in planning a method to solve this problem. (MP1, MP2, MP4) I only allow a few minutes, gauging by the frustration/anxiety level of the students before I suggest that maybe we need a way to solve for missing angles.  That leads us to the main activity of the day.

40 minutes