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The Graph of tan We are going to sketch the graph of where is an angle between and.
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38: The graph of 38: The graph of tantan
© Christine Crisp
““Teach A Level Maths”Teach A Level Maths”Vol. 1: AS Core Vol. 1: AS Core
ModulesModules
The Graph of tan
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Module C2
The Graph of tan
We are going to sketch the graph of where
tan
is an angle between and .
0 90
The Graph of tan
ysin
Draw a circle, radius 1, with centre at the origin and complete a triangle.
P (x, y)
x
y
O
y
1
Nx xcos
Also, xy
tan
So,
cossintan
To sketch the graph of we can divide values of and taken from their graphs.
tansin cos
From the triangle,and
The Graph of tan
tany
cosy
y
siny
y
00sin10cos
x
The graphs of and for are sin cos 3600
0
The Graph of tan
cosy
y
siny
y
x
The graphs of and for are sin cos 3600
x
0180sin1180cos 0
tany
The Graph of tan
siny
y
cosy
yx
The graphs of and for are sin cos 3600
x x
190sin090cos
This line, where is not defined is called an asymptote.
tan
tany
Dividing by zero gives infinity so is not defined when .
tan 90
The Graph of tan
siny
y
cosy
yx
The graphs of and for are sin cos 3600
x xx x
xx
tany
The Graph of tan
siny
y
cosy
yx
The graphs of and for are sin cos 3600
x xx x
xx
x x
x x
tany
The Graph of tan
siny
y
cosy
yx
The graphs of and for are sin cos 3600
x xx x
xx
x x
x x
tany
The Graph of tan
The graph of repeats every . . .tany 180
tany
The Graph of tan
is defined for angles less than and greater than in the same way as the other trig functions so the graph can be extended. e.g.
tan360
0
tany
. . . it is cyclic with a period of .180
The Graph of tan
Sketch the graph of for values of from to clearly showing the asymptotes.
tany180180
Exercise
(a)
30tantan
Use the graph to give a value of between and ( not equal to the given angle! ) where
(b)
160tantan
(c)
70tantan (d)
)40(tantan
Solution:
(a)
150
180180
x30
x150
The Graph of tan
Sketch the graph of for values of from to clearly showing the asymptotes.
tany180180
Exercise
(a)
30tantan
Use the graph to give a value of between and ( not equal to the given angle! ) where
(b)
160tantan
(c)
70tantan (d)
)40(tantan
(a)
150
180180
(b)
20x
160x
20
The Graph of tan
Sketch the graph of for values of from to clearly showing the asymptotes.
tany180180
Exercise
(a)
30tantan
Use the graph to give a value of between and ( not equal to the given angle! ) where
(b)
160tantan
(c)
70tantan (d)
)40(tantan
(a)
(b)
150
180180
20
x
70
(c)
70 110or x
110
x
70
The Graph of tan
Sketch the graph of for values of from to clearly showing the asymptotes.
tany180180
Exercise
(a)
30tantan
Use the graph to give a value of between and ( not equal to the given angle! ) where
(b)
160tantan
(c)
70tantan (d)
)40(tantan
(a)
(b)
(c)
150
180180
20
x
140
(c)
70 110or
(d)
140
x
40
The Graph of tan
The Graph of tan
The following slides contain repeats of information on earlier slides, shown without colour, so that they can be printed and photocopied.For most purposes the slides can be printed as “Handouts” with up to 6 slides per sheet.
The Graph of tan
Nysin
Draw a circle, radius 1, with centre at the origin and complete a triangle.
P (x, y)
x
y
O
y
1
x xcos
Also, xy
tan
So,
cossintan
To sketch the graph of we can divide values of and taken from their graphs.
tansin cos
From the triangle,and
The Graph of tan
The graph of repeats every . . .tany 180
tany
. . . it is cyclic with a period of .180