What do we need to What do we need to do?do?

What do we need to What do we need to change?change?

Graphing:Graphing:Secant and CosecantSecant and CosecantSection 4.5Section 4.5

csc (x)csc (x) Flip of sin (x)Flip of sin (x) PropertiesProperties

– Period: 2Period: 2– Domain: all real numbers except nDomain: all real numbers except n– Range: (-Range: (-∞, -1] [1, ∞)∞, -1] [1, ∞)– No x-intNo x-int– No y-intNo y-int– y=1 when y=1 when – y=-1 when y=-1 when

nx 223

nx 223

Graph of csc(x)Graph of csc(x)

GraphGraph 2)42

csc( y

GraphGraph 3)2csc( y

sec (x)sec (x) Flip of cos (x)Flip of cos (x) PropertiesProperties

– Period: 2Period: 2– Domain: all real numbers except n, n is Domain: all real numbers except n, n is

oddodd– Range: (-Range: (-∞, -1] [1, ∞)∞, -1] [1, ∞)– No x-intNo x-int– y-int = 1y-int = 1– Asymptotes when , n is oddAsymptotes when , n is odd– y=1 when , n is even y=1 when , n is even – y=-1 when , n is odd y=-1 when , n is odd

2

nx nx

2nx

Graph of sec (x)Graph of sec (x)

GraphGraph 2)63

sec( y

One last problem…One last problem… Write an equation for a secant Write an equation for a secant

function with period , phase function with period , phase shift shift vertical shift -3.vertical shift -3.

3

HomeworkHomework 4.5 Worksheet (csc and sec)4.5 Worksheet (csc and sec)