# Graph Matching Activity: Function, 1st & 2nd Derivatives - SINE AND COSINE

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SINE and COSINE Function graphs.

Students match the graphs of f(x), f'(x), and, f''(x) using only the characteristics of the graphs. The equations are provided in the teacher's solution sheet.

This is a collection of 30 graphs, ten sets of 3. All graphs are printed on the same size xy axes. Each graph is labeled, T01 through T30. The graphs are numbered randomly. The goal is to organize the graphs into sets of three which are f(x), f'(x), and, f''(x). You can, of course, use less than all ten sets at one time.

Arguments used are x, x/2, x/4, 2x, 2x+2, 4x, and x-π/4.

There are two graphs on each page. It is suggested that the graphs be printed, the pages cut in half and then laminated. The lamination will make them last a lot longer and the students can write on the laminated graphs with markers and not cause any damage. Keeping the graphs inside plastic sheet protectors would also work.

The functions are provided in the teacher's answer sheet. For example, Graph T01 is f(x )= - 4cos(2x); Graph T10 is f(x) = - 2sin(2x); and, Graph T29 is f(x) = cos(2x)-1. The solution sheet gives the equations and gives the three graphs of the set in order, f(x), f '(x), and, f ''(x), as shown in the product preview.

The graphs have a black Cartesian grid with the functions printed in blue. The y axis runs from --4 to 4; the x-axis runs from -2π to 2π.

Cover Sheet, 1 page
10 sets of 3 graphs, a total of 30 graphs (SIN and COSINE functions), 15 pages
Graphs of SIN(X), in red, and COS(X), in green, 1 page
Solutions and equations, 2 pages
Blank answer sheet for students, 1 page
Total 20 pages
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20 pages
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