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1: consider y=2tan(pi x  -  pi)                               ___     ____                              8          4a)find the period of the above equation and sketch a full cycle of the graph including asymptotes, and appropriate scales.

Question

1: consider y=2tan(pi x  -  pi)

                               ___     ____

                              8          4

a)find the period of the above equation and sketch a full cycle of the graph including asymptotes, and appropriate scales. 

check_circleAnswer
Step 1

Period does not depend on horizontal shift and vertical stretch.

Period= pi/b=pi/(pi/8)=8

period
b
=TX
=8
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Image Transcriptionclose

period b =TX =8

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Step 2

The graph has asymptotes when pi*x/8 - pi/4=pi/2

so, x=6

And at x=6-8=-2 there will be asymptote too

 

лх
п
л
4
2
лх
л
л
Or
8
4
2
Зл
лх
Or
8
4
Зл
Or, х-
4
л
Or, х-6
+
help_outline

Image Transcriptionclose

лх п л 4 2 лх л л Or 8 4 2 Зл лх Or 8 4 Зл Or, х- 4 л Or, х-6 +

fullscreen
Step 3

We draw from x=6-8=-2 to x=6, mak...

-2
0
2
4
6
X
2
|asymptote
0
asymptote
Y
-2
help_outline

Image Transcriptionclose

-2 0 2 4 6 X 2 |asymptote 0 asymptote Y -2

fullscreen

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Trigonometry

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