Start learning →

Simplify: arcsin(sin(x)) for x ∈ [π/2, π]:

A-x
Bπ - x (since sin(π-x) = sin x and π - x ∈ [0, π/2])
Cx
Dπ + x
Answer & Solution
Correct answer: B. π - x (since sin(π-x) = sin x and π - x ∈ [0, π/2])
For x ∈ [π/2, π]: sin x = sin(π - x), and π - x ∈ [0, π/2] which IS in arcsin's principal range. **So arcsin(sin x) = π - x.**
Practise this question with Quill — AP Intermediate 2nd Year →

Keep practising Probability & Statistics

Browse all Probability & Statistics questions for AP Intermediate 2nd Year, or explore more Mathematics topics.

Start a Probability & Statistics lesson →
Related questions
Number of solutions to arctan(x) = π/3 in real x:d/dx arcsin(sqrt(x)) =cos(2 arctan(x)) =arctan(x) - arctan(y) = (for xy > -1):d/dx [arctan(x²)] =Range of f(x) = arcsin(x) + arccos(x):Solve 2 arctan(x) = π/3: