4.6 Graphs of Other Trigonometric Functions csc, sec, tan, & cot Graphing csc and sec is done by...
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Transcript of 4.6 Graphs of Other Trigonometric Functions csc, sec, tan, & cot Graphing csc and sec is done by...
4.6Graphs of Other
Trigonometric Functionscsc, sec, tan, & cot
Graphing csc and sec is done by graphing its reciprocal function first.
Graph y = 3 + 2 csc ⎟⎠
⎞⎜⎝
⎛ +4
πx
v.s. = A =P =
h.s. =
32
πππ2
1
22==
n
4
π−
+ sin x
4
π− 4
7π4
9π−
Find the midpoint to locate y-axis.
4
3π
Draw vert. asy.
3
5
1
x-axis
4
π
What is the range and domain of y?
Range:
€
−∞,1( ] 5,∞[ )
Domain: To find the domain of csc x , set what comes
after csc = Ζ∈kk ,π
ππkx =+
4
Ζ∈−≠ℜ kkxD ,4
,:π
π
y = 2 – 4 sec (4x - ) πy = 2 – 4 sec 4(x - )
4
π
4
π
P = 2
π
4
3π4
π−
2
6
-2
v.s = 2 h.s. =4
π
A = 4
x-axis
Range: ( ] [ )∞−∞− ,62,
To find the domain, set what comes after sec =
Ζ∈+ kk ,2
ππ
πππ kx +=−2
4 ππkx +=
2
34
Ζ∈+≠ℜ kk
xD ,48
3,:
ππ
y = tan x
4
π2
π6
π3
π
1
-1
2
π−
4
π−
y = - tan x
Range: ℜDomain: set whatever is after the tan =
Ζ∈
+
k
k ,2
ππ
ππ==
nP
y = -3 tan 2x ππkx +≠
22 Ζ∈+≠ k
kx ,
24
ππ
Plug in –1, 0 and 1 for k to find vertical asymptotes.
v.a.’s at 4
3,
4,
4
πππ−
4
π−
4
π4
3π2
π
Range: ℜ
=P2
π
Range: ℜDomain: set whatever is after the cot = Ζ∈kk ,π
Period n
π= ππ
==1
y = cot x
Plug in -1, 0, and 1 for k to find the v.a.’s
Extra Sinusoid