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Find all angles, 0^(@) <= theta < 360^(@), that satisfy the equation below, to the nearest tenth of a degree. cot^(2)theta-1=0 Answer: theta=

Find all angles, 0^{\circ} \leq \theta<360^{\circ} , that satisfy the equation below, to the nearest tenth of a degree.\newlinecot⁡2θ−1=0 \cot ^{2} \theta-1=0 \newlineAnswer: θ= \theta=

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Csc, sec, and cot of special anglesright chevron icon

Full solution

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.\newlinecot⁡2θ−1=0 \cot ^{2} \theta-1=0 \newlineAnswer: θ= \theta=
  1. Solve Equation: Solve the equation cot⁡2(θ)−1=0\cot^2(\theta) - 1 = 0 for cot⁡2(θ)\cot^2(\theta).cot⁡2(θ)−1=0\cot^2(\theta) - 1 = 0⇒cot⁡2(θ)=1\Rightarrow \cot^2(\theta) = 1
  2. Take Square Root: Take the square root of both sides to solve for cot⁡(θ)\cot(\theta).cot⁡(θ)=±1\cot(\theta) = \pm 1
  3. Determine Angles: Determine the angles where cot⁡(θ)=1\cot(\theta) = 1 and cot⁡(θ)=−1\cot(\theta) = -1. For cot⁡(θ)=1\cot(\theta) = 1, θ\theta can be 45°45° or 225°225°. For cot⁡(θ)=−1\cot(\theta) = -1, θ\theta can be 135°135° or 315°315°.
  4. Verify Angles: Verify that all found angles are within the given range 0^\circ \leq \theta < 360^\circ. All angles 45∘45^\circ, 135∘135^\circ, 225∘225^\circ, and 315∘315^\circ are within the range.

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