Investigating the Graphs of Sine Functions.

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03.02.2004

Anna Markmann

Portfolio #2 - Type I

Investigating the Graphs of Sine Functions

The purpose of this assignment is to obtain general rules for transformations of sine functions from analysing patterns got from examples of these. To justify my conjectures of all of the following functions I used "Magic Graph" - an electronic graphing program which allowed me to present them with a high level of precision. The trigonometric settings and the radian mode were kept constant throughout the whole investigation.

Part 1

Graph of y= sin x

To present this graph properly there are several possibilities: one can use a graphing calculator, a computer program, draw the graph from tabled values or from the unit circle. I chose the unit circle method because it is then more understandable how sine of x gets its shape and position, since sine of an angle is the ratio of the length of the opposite side to the length of the hypotenuse and therefore1:

Characteristics of y= sin x

The sine curve is symmetric with the origin, it is an even function, and has infinite intercepts at multiples of , as