Unformatted text preview: Graphs of the Tangent
and Cotangent Function
and Section 10.3 part 2 y = tan x
tan
f( x) = tan( x) 3 2 1 2 2 1 2 3 4 y = cot x
cot
y = cot x 3 2 1 2 2 1 2 4 For y = a tan b(x +c) + d ; y = a cot b(x +c) + d a vertically stretches or shrinks the graph. The period is π . b
The phase shift is c units to the left if c > 0.
The
The phase shift is c units to the right if c < 0.
The
The vertical shift is d units up if d > 0.
The
The vertical shift is d units down if d < 0.
The Asymptotes
Asymptotes The tangent function has asymptotes 2n + 1 b( x + c ) = ÷π , if n is an integer .
2 The cotangent function has asymptotes b( x + c) = nπ , if n is an integer . Joke Time
Joke What is 7Q + 3Q? You’re welcome! How do hearing impaired people greet
How
one another?
one They sine waves! ...
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 Fall '08
 JARVIS
 Calculus, Phase Shift, Periodic function, Mathematical analysis, Sine wave

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