Graphs of Reciprocal Trigonometric Functions (Edexcel IAL Maths)

Reciprocal Trig Functions - Graphs

Spec point — 2.1

Graphs of reciprocal trigonometric functions

How do I sketch the graph of y = sec x?

• The graph of y = secx looks like this:

• y-axis **is a line of symmetry
• has period (ie repeats every) 360° or 2π 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

How do I sketch the graph of y = cosec x?

• The graph of y= cosec x looks like this:

• has period (ie repeats every) 360° or 2π 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

How do I sketch the graph of y = cot x?

• The graph of y= cot x looks like this:

• 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∈ ℝ (ie cot can take any real number value)

Exam Hint

• 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