Graphs of Other Trigonometric Functions

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Section 4.6

• Graphs of Other Trigonometric Functions

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Overview

• In this section we examine the graphs of the
  other four trigonometric functions.
• After looking at the basic, untransformed graphs
  we will examine transformations of tangent,
  cotangent, secant, and cosecant.
• Again, extensive practice at drawing these graphs
  using graph paper is strongly recommended.

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Tangent and Cotangent

• Three key elements of tangent and cotangent
• For which angles are tangent and cotangent equal
  to 0? These will be x-intercepts for your graph.
• For which angles are tangent and cotangent
  undefined? These will be locations for vertical
  asymptotes.
• For which angles are tangent and cotangent equal
  to 1 or -1? These will help to determine the
  behavior of the graph between the asymptotes.

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y tan x
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y cot x
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Transformations
A amplitude p/B period (distance between
asymptotes). C/B gives phase shift from zero.
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ExamplesGraph the Following
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Secant and Cosecant

• The graphs of secant and cosecant are derived
  from the graphs of cosine and sine, respectively
• Where sine and cosine are 0, cosecant and secant
  are undefined (location of vertical asymptotes).
• Where sine and cosine are 1, cosecant and secant
  are also 1.
• Where sine and cosine are -1, cosecant and secant
  are also -1.

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y csc x(derived from graph of y sin x)
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y sec x(derived from graph of y cos x)
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Transformations

• To graph a transformation of cosecant or secant,
  graph the transformation of sine or cosine,
  respectively, then use the reciprocal strategy
  previously discussed

A amplitude (affects the places where secant
or cosecant is equal to 1 or -1) 2p/B period
(distance between asymptotes) C/B phase
(horizontal) shift, left if (), right if (-)
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ExamplesGraph the Following