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# 4.5 sec and csc worked 3rd

graphing csc and sec

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### 4.5 sec and csc worked 3rd

1. 1. What do we need to do?What do we need to do?
2. 2. What do we need toWhat do we need to change?change?
3. 3. Graphing:Graphing: Secant and CosecantSecant and Cosecant Section 4.5Section 4.5
4. 4. 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 wheny=1 when – y=-1 wheny=-1 when π π nx π π 2 2 3 += nx ππ 2 2 3 +=
5. 5. Graph of csc(x)Graph of csc(x)
6. 6. GraphGraph 2) 42 csc( ++= πθ y
7. 7. GraphGraph 3)2csc( −+= πθy
8. 8. sec (x)sec (x)  Flip of cos (x)Flip of cos (x)  PropertiesProperties – Period: 2Period: 2 – Domain: all real numbers except n, n is oddDomain: all real numbers except n, n is odd – 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 eveny=1 when , n is even – y=-1 when , n is oddy=-1 when , n is odd π 2 π nx π= nx π= 2 n x π =
9. 9. Graph of sec (x)Graph of sec (x)
10. 10. GraphGraph 2) 63 sec( −+= πθ y
11. 11. One last problem…One last problem…  Write an equation for a secant functionWrite an equation for a secant function with period , phase shiftwith period , phase shift vertical shift -3.vertical shift -3. π 3 π
12. 12. HomeworkHomework  4.5 Worksheet (csc and sec)4.5 Worksheet (csc and sec)