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📐 Mathematics  ·  Inverse Trigonometric Functions  ·  JEE

Find the value of sin(cos-1(3/5)).

Answer: 4/5.

  • A 3/5
  • B 4/5
  • C 5/3
  • D 5/4

Correct answer: B. 4/5

Explanation: If theta = cos-1(3/5), then cos(theta) = 3/5, so the opposite side is sqrt(25-9) = 4, giving sin(theta) = 4/5.

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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