Domain and Range of Cosecant θ
Geometry
Level
2
What is the Domain and Range of the function f(θ) = Cosecant(θ) .
Note : Cosecant (θ) can be written in short form as cscθ
Cosecant θϵR, cscθ≤−1 or cscθ≥1
Cosecant θϵR, cscθ≥1
Cosecant θϵR,θ≠0,180,360… cscθ≤−1 or cscθ≥1
Cosecant θϵR, cscθ≤1 or cscθ≥-1
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1 solution
Cosecant(θ) or Csc(θ) is nothing but 1 /Sin(θ);
Sin(θ) is 0 for θ = 0 , 180, 360 etc., and hence for those values Csc(θ) is not defined.
Hence Csc(θ) exists over all values of (θ) except when θ = 0 , 180, 360 or where θϵR,θ≠0,180,360
Sin(θ) ranges between -1 and 1 and hence cscθ≤−1 or cscθ≥1