CIE A Level Maths: Pure 3復習筆記3.1.2 Reciprocal Trig Functions - Graphs
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?∈???(ie?cot?can take?any?real number value)
Exam 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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