4.5 sec and csc worked 3rd
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This document discusses the trigonometric functions csc(x) and sec(x). It provides properties of each function, including their period, domain, range, and any asymptotes or x-intercepts. Examples of graphs are shown for csc(x) with phase shifts of pi/2 and -pi/2. Properties of sec(x) are also described. The document concludes by assigning a worksheet on csc(x) and sec(x) and posing a problem to write an equation for a secant function with a given period, phase shift, and vertical shift.
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![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
+=](https://image.slidesharecdn.com/4-161103132924/85/4-5-sec-and-csc-worked-3rd-5-320.jpg)
![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
=](https://image.slidesharecdn.com/4-161103132924/85/4-5-sec-and-csc-worked-3rd-9-320.jpg)
4.5 sec and csc worked 3rd
- 2. What do we need to do?What do we need to do?
- 3. What do we need toWhat do we need to change?change?
- 4. Graphing:Graphing: Secant and CosecantSecant and Cosecant Section 4.5Section 4.5
- 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 wheny=1 when – y=-1 wheny=-1 when π π nx π π 2 2 3 += nx ππ 2 2 3 +=
- 6. Graph of csc(x)Graph of csc(x)
- 8. GraphGraph 3)2csc( −+= πθy
- 9. 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 =
- 10. Graph of sec (x)Graph of sec (x)
- 12. 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
- 13. HomeworkHomework 4.5 Worksheet (csc and sec)4.5 Worksheet (csc and sec)