# Inverse Trigonometric Functions - A Discovery Lesson

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This graphing calculator activity incorporates the TI84 or TI84C graphing calculator to discover the inverse function for the three basic trigonometric functions.

It begins with discovering some inverse functions that are not trigonometric. The first function explored is y = 2x + 1. Students learn that an inverse function can be found geometrically by reflecting a given function over the line y = x. Students try to do this by hand first. Then they are instructed that a geometric reflection can be done algebraically by replacing the variables x and y. So y = 2x +1 becomes x = 2y + 1. To indicate that this new equation is an inverse function new notation is introduced, f-1. Students solve the changed equation so y is a function of x. When they graph it, they find the original function is reflected over the line y = x.

Students then study the function y = (x + 5)2 in a similar way. When then solve the inverse function so y is a function of x they notice two square root expressions must be considered.

Students then move on to finding the inverse function for y = sin x, y = cos x, and y = tan x.

The Draw command, on the calculator, is used draw the inverse function after students first try to draw them.

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8 pages
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