3.1.2 Reciprocal Trig Functions - Graphs

What do graphs of the sec, cosec and cot look like?

• 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

• 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

• 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)