Reciprocal Trig Functions - Graphs (CIE A Level Maths: Pure 3)

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Reciprocal Trig Functions - Graphs

What does the graph of the sec look like?

  • The graph of = secx looks like this:

Recip Trig Graphs Illustr 1_sec, A Level & AS Maths: Pure revision notes

  • y-axis is a line of symmetry
  • has period (ie repeats every) 360° or radians
  • vertical asymptotes wherever cos x= 0
  • domain is all x except odd multiples of 90° (90°, -90°, 270°, -270°, etc.)
  • the domain in radians is all x except odd multiples of π/2 (π/2, - π/2, 3π/2, -3π/2, etc.)
  • range is y ≤ -1 or y ≥ 1

What does the graph of the cosec look like?

  • The graph of = cosec x looks like this:

Recip Trig Graphs Illustr 2_cosec, A Level & AS Maths: Pure revision notes

  • has period (ie repeats every) 360° or radians
  • vertical asymptotes wherever sin x= 0
  • domain is all x except multiples of 180° (0°, 180°, -180°, 360°, -360°, etc.)
  • the domain in radians is all x except multiples of π (0, π, - π, 2π, -2π, etc.)
  • range is y ≤ -1 or y ≥ 1

What does the graph of the cot look like?

  • The graph of = cot x looks like this:

 Recip Trig Graphs Illustr 3_cot, A Level & AS Maths: Pure revision notes

 

  • has period (ie repeats every) 180° or π radians
  • vertical asymptotes wherever tan x= 0
  • domain is all x except multiples of 180° (0°, 180°, -180°, 360°, -360°, etc.)
  • the domain in radians is all x except multiples of π (0, π, - π, 2π, -2π, etc.)
  • range is y   (ie cot can take any real number value)

Examiner Tip

  • Make sure you know the shapes of the graphs for cos, sin and tan.
  • The shapes of the reciprocal trig function graphs follow from those graphs plus the definitions sec = 1/cos, cosec = 1/sin and cot = 1/tan

Worked example

Recip Trig Graphs Example, A Level & AS Maths: Pure revision notes

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Roger

Author: Roger

Expertise: Maths

Roger's teaching experience stretches all the way back to 1992, and in that time he has taught students at all levels between Year 7 and university undergraduate. Having conducted and published postgraduate research into the mathematical theory behind quantum computing, he is more than confident in dealing with mathematics at any level the exam boards might throw at you.