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

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

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:

February 21, 2018

3. y = 2 tan 3x

period: ______

asymptotes & 3-key points:

4. Determine period and equation of the tangent function.

Period _______

equation: ____________

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

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