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Graphs of other trigonometric functions. Advanced Math 6.5. Tangent curve. Let’s graph it Amplitude – undefined Period – p Range (-∞, ∞). Tangent. Sketching tangent graphs. Find two vertical asymptotes and the x-intercept between them

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tangent curve
Tangent curve
  • Let’s graph it
  • Amplitude – undefined
  • Period – p
  • Range (-∞, ∞)

Advanced Math 6.4

tangent
Tangent

Advanced Math 6.4

sketching tangent graphs
Sketching tangent graphs
  • Find two vertical asymptotes and the x-intercept between them
  • Plot a few additional points between the asymptotes to sketch one cycle
  • Add additional cycles to the right and left

Advanced Math 6.4

examples
Examples

Advanced Math 6.4

cotangent curve
Cotangent curve
  • Let’s graph it
  • Amplitude – undefined
  • Period – p
  • Range (-∞, ∞)

Advanced Math 6.4

cotangent
Cotangent

Advanced Math 6.4

sketching cotangent graphs
Sketching cotangent graphs
  • Find two vertical asymptotes and the x-intercept
  • Plot a few additional points between the asymptotes to sketch one cycle
  • Add additional cycles to the right and left

Advanced Math 6.4

example
Example

Advanced Math 6.4

cosecant
Cosecant
  • Reciprocal of sine
  • Start by graphing the sine curve
  • csc curve has V.A. where sin curve has x-intercepts
  • max. on sin curve are min. on csc curve
  • min. on sin curve are max. on csc curve

Advanced Math 6.4

examples1
Examples

Advanced Math 6.4

secant
Secant
  • Reciprocal of cosine
  • Start by graphing the cosine curve
  • sec curve has V.A. where cos curve has x-intercepts
  • max. on cos curve are min. on sec curve
  • min. on cos curve are max. on sec curve

Advanced Math 6.4

examples2
Examples

Advanced Math 6.4