More Trigonometric Graphs 5.4 Essential Question: How are secant and cosecant graphs related to sine and cosine graphs?

Tangent and Cotangent Graph Properties Period: Asymptotes: Cotangent Period: Asymptotes:

Graphing Tangent and Cotangent functions: Find the amplitude, period, left asymptote, and right asymptote. Make an x-y chart: 1st x-coordinate: use the left asymptote. 5th x-coordinate: use the right asymptote. 3rd x-coordinate: find the midpoint of the 1st and 5th coordinates. 2nd x-coordinate: find the midpoint of the 1st and 3rd coordinates. 4th x-coordinate: find the midpoint of the 5th and 3rd corrdinates.

Graphing Cont’d Substitute the x-coordinates into the original function to find y. Draw the asymptotes. Plot the points in a coordinate plane. Connect the dots with a smooth curve.

Examples: Graph the following functions

Graphing Cosecant and Secant Graph the sine or cosine function first. Draw asymptotes. (Hint: there will be an asymptote anywhere the sine or cosine function crosses the x-axis.) Interchange “hills” and “valleys”. A “hill” on sine or cosine will become a “valley” on cosecant or secant. A “valley” on sine or cosine will become a “hill” on cosecant or secant.

Graph of Cosecant

Graph of Secant

Examples: Graph the following functions.