Inverse Trigonometric Functions

Basic Concepts of Inverse Trigonometric Functions


  • Sin−1 (Sin x) = x ∀ x ∈ \left[-\frac{\pi}{2},\frac{\pi}{2}\right]
  • Sin (Sin−1x) = x ∀ x ∈ [−1, 1]
  • Cos−1(Cos x) = x ∀ x ∈ [0, π]
    Cos(Cos−1x) = x ∀ x ∈ [−1, 1]
  • Tan−1 (Tan x) = x ∀ x ∈ \left(-\frac{\pi}{2},\frac{\pi}{2}\right)
    Tan (Tan−1x) = x ∀ x ∈ R
  • Cot−1(Cot x) = x ∀ x ∈ (0, π)
    Cot(Cot−1x) = x ∀ x ∈ R
  • Sec−1(Sec x) = x ∀ x ∈ [0, π] − \left\{\frac{\pi}{2}\right\}
    Sec(Sec−1x) = x ∀ x ∈ R − (−1, 1)
  • Cosec−1(Cosec x) = x ∀ x ∈ \left[-\frac{\pi}{2},\frac{\pi}{2}\right] - {0}
    Cosec(Cosec−1 x) = x ∀ x ∈ R − (−1, 1)

Part1: View the Topic in this video From 00:40 To 57:48

Part2: View the Topic in this video From 00:40 To 16:30

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  • Domain and Range of Inverse Trigonometric functions:
FUNCTION DOMAIN RANGE
Sin−1 x [−1, 1] \left[-\frac{\pi}{2},\frac{\pi}{2}\right]
Cos−1 x [−1, 1] [0, π]
Tan−1 x R \left(-\frac{\pi}{2},\frac{\pi}{2}\right)
Cot−1 x R (0, π)
Sec−1 x R − (−1, 1) [0, π] − \left\{\frac{\pi}{2}\right\}
Cosec−1 x R − (−1, 1) \left[-\frac{\pi}{2},\frac{\pi}{2}\right] - {0}