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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. −14cos⁡(θ)+7=0-14\cos(\theta)+7=0

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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. −14cos⁡(θ)+7=0-14\cos(\theta)+7=0
  1. Isolate cos⁡(θ)\cos(\theta): Step 11: Isolate cos⁡(θ)\cos(\theta) in the equation.\newlineStarting with 14cos⁡(θ)+7=014\cos(\theta) + 7 = 0, subtract 77 from both sides to get 14cos⁡(θ)=−714\cos(\theta) = -7.\newlineThen, divide both sides by 1414 to isolate cos⁡(θ)\cos(\theta): cos⁡(θ)=−714\cos(\theta) = -\frac{7}{14}, which simplifies to cos⁡(θ)=−12\cos(\theta) = -\frac{1}{2}.
  2. Find values of θ\theta: Step 22: Find the values of θ\theta that satisfy cos⁡(θ)=−12\cos(\theta) = -\frac{1}{2} within the given interval.\newlinecos⁡(θ)=−12\cos(\theta) = -\frac{1}{2} occurs at specific standard angles. In the interval 0≤θ≤π0\leq\theta\leq\pi, the angle that satisfies this is θ=2π3\theta = \frac{2\pi}{3}.

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