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Find all angles, 0^(@) <= theta < 360^(@), that satisfy the equation below, to the nearest tenth of a degree. sin^(2)theta-sin 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.\newlinesin⁡2θ−sin⁡θ=0 \sin ^{2} \theta-\sin \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.\newlinesin⁡2θ−sin⁡θ=0 \sin ^{2} \theta-\sin \theta=0 \newlineAnswer: θ= \theta=
  1. Factor Trigonometric Equation: Factor the given trigonometric equation. sin⁡2(θ)−sin⁡(θ)=0\sin^2(\theta) - \sin(\theta) = 0 can be factored as sin⁡(θ)⋅(sin⁡(θ)−1)=0\sin(\theta) \cdot (\sin(\theta) - 1) = 0.
  2. Set Factors Equal: Set each factor equal to zero to find the solutions for θ\theta.sin⁡(θ)=0\sin(\theta) = 0 and sin⁡(θ)−1=0\sin(\theta) - 1 = 0.
  3. Solve for Theta: Solve the first equation sin⁡(θ)=0\sin(\theta) = 0. The sine function is zero at 00 degrees, 180180 degrees, and 360360 degrees.
  4. Find Solutions: Solve the second equation sin⁡(θ)−1=0\sin(\theta) - 1 = 0. This simplifies to sin⁡(θ)=1\sin(\theta) = 1, which occurs at 9090 degrees.
  5. Compile All Solutions: Compile all the solutions.\newlineThe angles that satisfy the equation are 00 degrees, 9090 degrees, 180180 degrees, and 360360 degrees.

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