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📐 Mathematics  ·  Inverse Trigonometric Functions  ·  JEE

The principal value range of sin-1 x is:

Answer: [-pi/2, pi/2].

  • A [0, pi]
  • B [-pi/2, pi/2]
  • C (-pi/2, pi/2)
  • D [-pi, pi]

Correct answer: B. [-pi/2, pi/2]

Explanation: sin-1 x has principal value branch [-pi/2, pi/2], with domain [-1,1].

y = sin⁻¹x: Principal Value Branchxyx=-1x=1y=-π/2y=π/2Domain restricted to [-1,1]; range restricted to [-π/2,π/2] - this restriction is what makes the inverse exist

The graph of sin⁻¹x is confined to a narrow domain [-1,1] (since sine itself only takes values in that range) and range [-π/2,π/2] (the principal value branch chosen to make sine one-one and invertible there).

Concept context

Restricting trig functions to make them invertible, the principal value branches of sin-inverse, cos-inverse, tan-inverse, and friends, and the key identities relating them.

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