Question

Question 1: Find the principal value of sin¯¹ (-1/2)

Class 12 - Math - Inverse Trigonometric Functions

Answer 1

let sin-¹(-1/2) = ∅ ,where ∅ is the principal value of sin-¹(-1/2)
=> sin∅ = -1/2

Since the range of the principal value branch of sin-¹x is [-π/2,π/2] , therefore
-π/2≤0≤π/2
Now, sin∅ = -1/2 = -sinπ/6 = sin(-π/6)
∅ = -π/6
as sin(-π/6) = -1/2 and -π/6€ [-π/2,π/2]

Hence principal value of sin-¹(-1/2) is -π/6