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Find all solutions with −90°≤θ≤90°-90° \leq \theta \leq 90°. Give the exact answer(s) in simplest form. If there are multiple answers, separate them with commas.\newlinesin⁡(θ)=12\sin (\theta) = \frac{1}{2}\newline___°

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Q. Find all solutions with −90°≤θ≤90°-90° \leq \theta \leq 90°. Give the exact answer(s) in simplest form. If there are multiple answers, separate them with commas.\newlinesin⁡(θ)=12\sin (\theta) = \frac{1}{2}\newline___°
  1. Identify Standard Angle: We know that sin⁡(θ)=12\sin(\theta) = \frac{1}{2} at specific standard angles. The unit circle helps us remember that sin⁡(30°)=12\sin(30°) = \frac{1}{2}.
  2. Consider Negative Angles: Since we're looking for angles between −90∘-90^\circ and 90∘90^\circ, we also need to consider negative angles. The sine function is positive in the first and second quadrants. So, we need to find the angle in the second quadrant that has the same sine value.
  3. Find Corresponding Angle: The corresponding angle in the second quadrant is 180°−30°180° - 30°, which is 150°150°. But this is outside our range of −90°-90° to 90°90°, so we won't include it.

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