Perplex
Content
  • Exponents & Logarithms
  • Approximations & Error
  • Sequences & Series
  • Counting & Binomials
  • Proof and Reasoning
  • Complex Numbers
  • Cartesian plane & lines
  • Quadratics
  • Function Theory
  • Transformations & asymptotes
  • Polynomials
  • 2D & 3D Geometry
  • Trig equations & identities
  • Vectors
  • Probability
  • Descriptive Statistics
  • Distributions & Random Variables
  • Differentiation
  • Integration
  • Differential Equations
  • Maclaurin
Other
  • Review Videos
  • Formula Booklet
  • Blog
  • Landing Page
  • Sign Up
  • Login
  • Perplex
    IB Math AAHL
    /
    Trig equations & identities
    /

    Reciprocal trig functions

    Edit

    Exercises

    Key Skills

    Reciprocal trig functions

    Reciprocal trig functions

    The functions ​secx, ​cosecx​ and ​cotx, domain, range & graphs

    Want a deeper conceptual understanding? Try our interactive lesson! (Plus Only)

    Exercises

    No exercises available for this concept.

    Practice exam-style reciprocal trig functions problems

    Key Skills

    Reciprocal Trig Ratios
    AHL 3.9

    The reciprocal trig functions are functions of the form ​f(x)1​, where ​f​ is ​sin,cos​ or ​tan. The three reciprocal trig functions are:

    ​
    secθ cosecθ cotθ​=cosθ1​📖 =sinθ1​📖 =tanθ1​📖​
    ​
    Graph & domain & range of sec(x)
    AHL 3.9

    ​secx​

    Powered by Desmos

    • Domain: ​x=2(2k+1)π​=±2π​,±23π​…​

    • Range: ​secx≤−1​ or ​secx≥1.

    Graph & domain & range of cosec(x)
    AHL 3.9

    ​cosecx​

    Powered by Desmos

    • Domain: ​x=kπ=0,±π,±2π…​

    • Range: ​cosecx≤−1​ or ​cosecx≥1.

    Graph & domain & range of cot(x)
    AHL 3.9

    ​cotx​

    Powered by Desmos

    • Domain: ​x=kπ=0,±π,±2π…​

    • Range: ​cotx∈R.