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February 21, 2018
Algebra 214.1 Graphing tangent functions
Learning Target:I can graph & analyze tangent functions. [F.IF.7e & F.BF.3]
(1,0)
(0,–1)
(–1,0)
(0,1)
•
•
•
•
(√22
√22
, )√22
– √22( ),
√22
–√22
, )(( )√2
2–
√22
– ,
π/4π/2
3π/4
π
5π/43π/2
7π/4
y = tan x =
x y0
π/4
π/2
3π/4π
5π/4
3π/2
7π/4
2π
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February 21, 2018
Recall the graph of y = tan x:
period: ________
Note the asymptotes & 3 key points:
You can use the asymptotes & three "key points" equally spaced through one cycle to sketch a tangent curve.
This pattern is asymptote - (-a) - zero - (a) - asymptote.
Suppose y = a tan bx with a ≠ 0, and b > 0 and x is in radians, then
– is the period of the function.
– one cycle occurs in the interval from - to .
– Vertical asymptotes at end of each cycle.
bπ
2bπ
2bπ
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February 21, 2018
Graph each tangent function.
1. y = tan x23
period: ______
asymptotes & 3-key points:
2. y = tan 2x
period: ______
asymptotes & 3-key points:
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February 21, 2018
3. y = 2 tan 3x
period: ______
asymptotes & 3-key points:
4. Determine period and equation of the tangent function.
Period _______
equation: ____________
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February 21, 2018
Assignment:
14.1 Graphing trig functions worksheet
14.1 WS #4 Graphing tangent ANSWERS
1. period = π/2
eqn. y = 4 tan 2x2. period = 1/2
eqn. y = 2 tan 2πx3. period = π
eqn. y = 2 tan x
4. period = π
x = –π/2 (–π/4, –2)
(0,0)
(π/4, 2) x = π/2
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February 21, 2018
5. period = 2π
x = –π (–π/2, –3)
(0,0)
(π/2, 3) x = π
6. period = π/3
x = –π/6 (–π/12, –4) (0,0)
(π/12, 4) x = π/6
7. y = tan 4x
8. y = 2 tan x14