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Find all angles, 0^(@) <= theta < 360^(@), that satisfy the equation below, to the nearest tenth of a degree. cos^(2)theta-2cos theta=0 Answer: theta=

Find all angles, 0^{\circ} \leq \theta<360^{\circ} , that satisfy the equation below, to the nearest tenth of a degree.\newlinecos⁡2θ−2cos⁡θ=0 \cos ^{2} \theta-2 \cos \theta=0 \newlineAnswer: θ= \theta=

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Csc, sec, and cot of special anglesright chevron icon

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Q. Find all angles, 0∘≤θ<360∘ 0^{\circ} \leq \theta<360^{\circ} , that satisfy the equation below, to the nearest tenth of a degree.\newlinecos⁡2θ−2cos⁡θ=0 \cos ^{2} \theta-2 \cos \theta=0 \newlineAnswer: θ= \theta=
  1. Factor equation: Factor the given equation cos⁡2(θ)−2cos⁡(θ)=0\cos^2(\theta) - 2\cos(\theta) = 0. We can factor out cos⁡(θ)\cos(\theta) from both terms. cos⁡(θ)(cos⁡(θ)−2)=0\cos(\theta)(\cos(\theta) - 2) = 0
  2. Solve for theta: Set each factor equal to zero and solve for theta.\newlinecos⁡(θ)=0\cos(\theta) = 0 and cos⁡(θ)−2=0\cos(\theta) - 2 = 0\newlineFor cos⁡(θ)=0\cos(\theta) = 0, the angles where the cosine of theta is zero are 90∘90^\circ and 270∘270^\circ.\newlineFor cos⁡(θ)−2=0\cos(\theta) - 2 = 0, we add 22 to both sides to get cos⁡(θ)=2\cos(\theta) = 2. However, the cosine of an angle cannot be greater than 11 or less than −1-1, so there are no solutions from this part.
  3. Compile solutions: Compile the solutions.\newlineThe angles that satisfy the equation are 90∘90^\circ and 270∘270^\circ.

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