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Find all solutions with 0≤θ≤π0\leq\theta\leq\pi. Give the exact answer(s) in simplest form. If there are multiple answers, separate them with commas. –7sec⁡(θ)–7=0– 7\sec(\theta)–7=0

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Full solution

Q. Find all solutions with 0≤θ≤π0\leq\theta\leq\pi. Give the exact answer(s) in simplest form. If there are multiple answers, separate them with commas. –7sec⁡(θ)–7=0– 7\sec(\theta)–7=0
  1. Simplify equation: Simplify the equation −7sec⁡(θ)−7=0-7\sec(\theta)-7=0 by adding 77 to both sides.\newline−7sec⁡(θ)=7-7\sec(\theta) = 7\newlinesec⁡(θ)=−1\sec(\theta) = -1
  2. Rewrite using sec: Recall that sec⁡(θ)=1cos⁡(θ)\sec(\theta) = \frac{1}{\cos(\theta)}, so rewrite the equation.\newline1cos⁡(θ)=−1\frac{1}{\cos(\theta)} = -1\newlinecos⁡(θ)=−1\cos(\theta) = -1
  3. Determine solution: Determine where cos⁡(θ)=−1\cos(\theta) = -1 within the interval 0≤θ≤π0\leq\theta\leq\pi.\newlinecos⁡(θ)=−1\cos(\theta) = -1 at θ=π\theta = \pi

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