Graphs of Reciprocal Trigonometric Functions (OCR A Level Maths A): Revision Note

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)