Question

If 2 cos⁻¹x = y, then ______.

Options

• 0 ≤ y ≤ π

• −π ≤ y ≤ π

• 0 ≤ y ≤ 2π

• −π ≤ y ≤ 0

Answer 1

If 2 cos⁻¹x = y, then 0 ≤ y ≤ 2π.

Explanation:

The principal value range of cos⁡⁻¹x is [0, π]. Let cos⁡⁻¹x = θ, so θ ∈ [0, π].

Then, y = 2θ, giving y ∈ [0, 2π].