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Find all solutions with −π2≤θ≤π2 - \frac{\pi}{2} \leq \theta \leq \frac{\pi}{2} . Give the exact answer(s) in simplest form. If there are multiple answers, separate them with commas. csc⁡(θ)=1 \csc(\theta)=1

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Q. Find all solutions with −π2≤θ≤π2 - \frac{\pi}{2} \leq \theta \leq \frac{\pi}{2} . Give the exact answer(s) in simplest form. If there are multiple answers, separate them with commas. csc⁡(θ)=1 \csc(\theta)=1
  1. Understand csc(θ):csc(\theta): Step 11: Understand the function csc(θ)csc(\theta) and its relation to sin⁡(θ)\sin(\theta). csc(θ)=1sin⁡(θ)csc(\theta) = \frac{1}{\sin(\theta)}. We need to find θ\theta such that csc(θ)=1csc(\theta) = 1, which implies sin⁡(θ)=1\sin(\theta) = 1.
  2. Find θ\theta for csc⁡(θ)=1\csc(\theta) = 1: Step 22: Recall the values of θ\theta where sin⁡(θ)=1\sin(\theta) = 1 within the interval −π2≤θ≤π2-\frac{\pi}{2} \leq \theta \leq \frac{\pi}{2}. The only angle where sin⁡(θ)=1\sin(\theta) = 1 in this interval is θ=π2\theta = \frac{\pi}{2}.

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