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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. −7sin⁡(θ)−72=0-7\sin(\theta)-\frac{7}{2}=0

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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. −7sin⁡(θ)−72=0-7\sin(\theta)-\frac{7}{2}=0
  1. Isolate sin⁡(θ)\sin(\theta): Simplify the equation by isolating sin⁡(θ)\sin(\theta). Start by adding 72\frac{7}{2} to both sides:\newline-7\sin(\theta) – \frac{7}{2} + \frac{7}{2} = 0 + \frac{7}{2},\(\newline-7\sin(\theta) = \frac{7}{2}.\)
  2. Divide by −7-7: Divide both sides by −7-7 to solve for sin⁡(θ)\sin(\theta):sin⁡(θ)=72/−7\sin(\theta) = \frac{7}{2} / -7,sin⁡(θ)=−12\sin(\theta) = -\frac{1}{2}.
  3. Determine relevant angle: Determine the angles θ\theta for which sin⁡(θ)=−12\sin(\theta) = -\frac{1}{2} within the interval –90°≤θ≤90°–90°\leq\theta\leq90°. The sine function equals −12-\frac{1}{2} at specific standard angles. In the given range, the relevant angle is: θ=−30°\theta = -30°.

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