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Mathematics

Secondary 5 • June 1, 2025

I found: " In [0,2π], θ₁ = sin⁻¹ (k) and θ₂ = π - θ₁ ; In ℝ, S = {θ₁, + 2πn, θ₂ + 2πn, n∈ℤ} " in the section about sin functions. Can you help me understand what this means, and what we're solving here?

Answer (1)

Alloprof Answer

June 3, 2025

Hi. Thanks for your question. That's a surprising formulation. Let's make it step by step.
First step.
When you read θ₁ = sin⁻¹ (k) , it simply means
k = sin θ₁
Second step.
The range of θ₁ = sin⁻¹ (k) is [0, 2π]. Therefore, the range of k = sin θ₁ must be [-1, 1].
The problem is now in the formulation we usually see in problems.
You just have to use the technique explained in our video to finish the problem. Consider both the periodicity and symmetry to make the general solution.
Don't hesitate to come back if you have other questions.
Have a nice day.
Denis P.
https://www.youtube.com/watch?v=AP0MOuCahk8