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Find all solutions with - \frac{\pi}{2} < \theta < \frac{\pi}{2} . Give the exact answer(s) in simplest form. If there are multiple answers, separate them with commas. −7tan⁡(θ)+7=0 - 7\tan(\theta) + 7 = 0

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Q. Find all solutions with −π2<θ<π2 - \frac{\pi}{2} < \theta < \frac{\pi}{2} . Give the exact answer(s) in simplest form. If there are multiple answers, separate them with commas. −7tan⁡(θ)+7=0 - 7\tan(\theta) + 7 = 0
  1. Simplify equation: Simplify the equation −7tan⁡(θ)+7=0-7\tan(\theta) + 7 = 0 to find tan⁡(θ)\tan(\theta).\newline−7tan⁡(θ)+7=0-7\tan(\theta) + 7 = 0\newline−7tan⁡(θ)=−7-7\tan(\theta) = -7\newlinetan⁡(θ)=1\tan(\theta) = 1
  2. Find tan⁡(θ):\tan(\theta): Determine the values of θ\theta where tan⁡(θ)=1\tan(\theta) = 1 within the interval −π2-\frac{\pi}{2} to π2\frac{\pi}{2}.\newlinetan⁡(θ)=1\tan(\theta) = 1 at θ=π4\theta = \frac{\pi}{4} and θ=−3π4\theta = -3\frac{\pi}{4}; however, −3π4-3\frac{\pi}{4} is not within the interval −π2-\frac{\pi}{2} to π2\frac{\pi}{2}.\newlineSo, θ=π4\theta = \frac{\pi}{4} is the only solution in the given interval.

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