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Find all solutions with −90∘≤θ≤90∘-90^\circ\leq\theta\leq90^\circ. Give the exact answer(s) in simplest form. If there are multiple answers, separate them with commas. −2sin⁡(θ)+92=−13sin⁡(θ)+10-2\sin(\theta)+\frac{9}{2}=-13\sin(\theta)+10

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Full solution

Q. Find all solutions with −90∘≤θ≤90∘-90^\circ\leq\theta\leq90^\circ. Give the exact answer(s) in simplest form. If there are multiple answers, separate them with commas. −2sin⁡(θ)+92=−13sin⁡(θ)+10-2\sin(\theta)+\frac{9}{2}=-13\sin(\theta)+10
  1. Simplify Equation: Simplify the equation −2sin⁡(θ)+92=−13sin⁡(θ)+10-2\sin(\theta) + \frac{9}{2} = -13\sin(\theta) + 10.
  2. Isolate sin⁡(θ)\sin(\theta): Isolate sin⁡(θ)\sin(\theta) on one side.
  3. Divide by 1111: Divide both sides by 1111 to solve for sin⁡(θ)\sin(\theta).
  4. Find θ\theta: Find θ\theta within the interval –90°≤θ≤90°–90°\leq\theta\leq90° where sin⁡(θ)=12\sin(\theta) = \frac{1}{2}.

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