Zaymiey

📐 Mathematics  ·  Inverse Trigonometric Functions  ·  JEE

The principal value range of cos⁻¹(x) is:

Answer: [0, π].

  • A [0, π]
  • B [−π/2, π/2]
  • C [−π, π]
  • D [0, 2π]

Correct answer: A. [0, π]

Explanation: The principal branch of arccosine is [0, π].

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.

Read the full Inverse Trigonometric Functions notes →