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Find all solutions with −90∘≤θ≤90∘-90^\circ \leq \theta \leq 90^\circ. Give the exact answer(s) in simplest form. If there are multiple answers, separate them with commas.\newlinecsc⁡(θ)=−1\csc(\theta) = -1\newline____ ∘\_\_\_\_\,^\circ

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Q. Find all solutions with −90∘≤θ≤90∘-90^\circ \leq \theta \leq 90^\circ. Give the exact answer(s) in simplest form. If there are multiple answers, separate them with commas.\newlinecsc⁡(θ)=−1\csc(\theta) = -1\newline____ ∘\_\_\_\_\,^\circ
  1. Identify Angle: csc⁡(θ)=−1\csc(\theta) = -1\newlineIdentify the angle where the value of cosecant is −1-1.\newlineThe cosecant function is the reciprocal of the sine function, so csc⁡(θ)=1sin⁡(θ)\csc(\theta) = \frac{1}{\sin(\theta)}. Therefore, we are looking for angles where sin⁡(θ)=−1\sin(\theta) = -1.
  2. Find Minimum Point: Find the angle within the given range where sin⁡(θ)=−1\sin(\theta) = -1. The sine function reaches a value of −1-1 at its minimum point in its cycle. Within the range –90°≤θ≤90°–90° \leq \theta \leq 90°, this occurs at θ=−90°\theta = -90°.
  3. Verify Solution: Verify that the solution is within the given range.\newlineThe angle θ=−90∘\theta = -90^\circ is within the range −90∘≤θ≤90∘-90^\circ \leq \theta \leq 90^\circ.

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