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Find all solutions with - 90°<\theta<90° . Give the exact answer(s) in simplest form. If there are multiple answers, separate them with commas. 2tan⁡(θ)=0 2\tan(\theta)=0

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Full solution

Q. Find all solutions with −90°<θ<90° - 90°<\theta<90° . Give the exact answer(s) in simplest form. If there are multiple answers, separate them with commas. 2tan⁡(θ)=0 2\tan(\theta)=0
  1. Convert to radians: Convert the angle range from degrees to radians for consistency with the tangent function; −90°-90° is −π2-\frac{\pi}{2} and 90°90° is π2\frac{\pi}{2}.
  2. Set up equation: Set up the equation based on the problem statement: 2tan⁡(θ)=02\tan(\theta) = 0.
  3. Simplify equation: Simplify the equation by dividing both sides by 22 to isolate tan⁡(θ)\tan(\theta): tan⁡(θ)=0\tan(\theta) = 0.
  4. Solve for θ\theta: Solve for θ\theta where tan⁡(θ)=0\tan(\theta) = 0 within the interval -\frac{\pi}{2} < \theta < \frac{\pi}{2}. The tangent function is zero at θ=0\theta = 0.
  5. Check for solutions: Check for other possible solutions within the interval. The tangent function has a period of π\pi, but adding or subtracting π\pi from 00 would fall outside the given interval.

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