graphing csc and sec

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)

7. GraphGraph 2)
42
csc( ++=
πθ
y

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)

11. GraphGraph 2)
63
sec( −+=
πθ
y

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)