4.5 sec and csc worked 3rd
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Transcript of 4.5 sec and csc worked 3rd
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
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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.
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HomeworkHomework 4.5 Worksheet (csc and sec)4.5 Worksheet (csc and sec)