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📐 Mathematics  ·  Inverse Trigonometric Functions  ·  JEE

Find the principal value of cot-1(-1).

Answer: 3pi/4.

  • A pi/4
  • B 3pi/4
  • C -pi/4
  • D pi/2

Correct answer: B. 3pi/4

Explanation: cot(3pi/4) = -1, and 3pi/4 lies in the principal range (0,pi), so cot-1(-1) = 3pi/4.

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 →