Graphs of Secant, Cosecant, Tangent, and Cotangent

Tangent Function: y = tan x

• One cycle occurs between -p/2 and p/2
• There are vertical asymptotes at each end of the cycle

The asymptote that occurs at p/2 repeats every p units

• Period = p
• Amplitude = none, graphs go on forever in vertical directions

Cotangent Function: y = cot x

• One cycle occurs between 0 and p
• There are vertical asymptotes at each end of the cycle

The asymptote that occurs at p repeats every p units

• Period = p
• Amplitude = none, graphs go on forever in vertical directions

Cosecant Function: y = csc x

• There are vertical asymptotes.  The asymptote that occurs at p repeats every p units.
• Period = 2p
•  Amplitude:  none, graphs go on forever in vertical directions.
• The maximum values of y = sin x are minimum values of the positive sections of y = csc x.  The minimum values of y = sin x are the maximum values of the negative sections of y = csc x.
• The x-intercepts of y = sin x are the asymptotes for y = csc x.

Secant Function: y = sec x

• There are vertical asymptotes.  The asymptote that occurs at p repeats every p units.
• Period = 2p
• Amplitude:  none, graphs go on forever in vertical directions.
• The maximum values of y = cos x are minimum values of the positive sections of y = sec x.  The minimum values of
  y = cos x are the maximum values of the negative sections of
  y = sec x.
• The x-intercepts of y = cos x are the asymptotes for 
  y = sec x.

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