Generating the Graphs of the Generating the Graphs of the Trigonometric FunctionsTrigonometric Functions

By: Christopher ImmBy: Christopher Imm

Generating the graphs of sine, cosine, and Generating the graphs of sine, cosine, and tangenttangent

• The graphs of sine and cosine may be The graphs of sine and cosine may be generated by the unit circle.generated by the unit circle.

• In the following movies, note that the In the following movies, note that the cosine of cosine of xx is the evolution of the is the evolution of the x x or or horizontal component on the unit circle.horizontal component on the unit circle.

• The sine or The sine or xx is the evolution of the is the evolution of the yy or or vertical component on the unit circle.vertical component on the unit circle.

• Think of the input of the function as a time Think of the input of the function as a time component.component.

The graph of cosine of The graph of cosine of xx

The graph of sine of The graph of sine of xx

The graph of tangent of The graph of tangent of xx• Tangent is more difficult to visualize, but Tangent is more difficult to visualize, but

remember it is the ratio of sine to cosine.remember it is the ratio of sine to cosine.

Trigonometric Gallery Trigonometric Gallery WebsiteWebsite

http://http://mathdemos.gcsu.edu/mathdemos/family_of_functions/mathdemos.gcsu.edu/mathdemos/family_of_functions/trig_gallery.htmltrig_gallery.html