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Reciprocal Trig Functions - Graphs (CIE A Level Maths: Pure 3)
Revision Note
Reciprocal Trig Functions - Graphs
What does the graph of the sec 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
What does the graph of the cosec look like?
- 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
What does the graph of the cot look like?
- 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)
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
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