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Find all angles, 0^(@) <= theta < 360^(@), that solve the following equation. tan theta=sqrt3 Answer: theta=

Find all angles, 0∘≤θ<360∘ 0^{\circ} \leq \theta<360^{\circ} , that solve the following equation.\newlinetan⁡θ=3 \tan \theta=\sqrt{3} \newlineAnswer: θ= \theta=

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Q. Find all angles, 0∘≤θ<360∘ 0^{\circ} \leq \theta<360^{\circ} , that solve the following equation.\newlinetan⁡θ=3 \tan \theta=\sqrt{3} \newlineAnswer: θ= \theta=
  1. Recognize Equation: Recognize that the equation tan⁡(θ)=3\tan(\theta) = \sqrt{3} is looking for angles where the tangent function has the value of 3\sqrt{3}. The tangent function has the value of 3\sqrt{3} at angles where the opposite side over the adjacent side of a right triangle equals 3\sqrt{3}, which corresponds to an equilateral triangle cut in half, forming a 3030-6060-9090 triangle. Therefore, the reference angle for which tan⁡(θ)=3\tan(\theta) = \sqrt{3} is 6060 degrees.
  2. Find Reference Angle: Determine the angles in the interval [0,360)[0, 360) degrees where the tangent function is positive.\newlineTangent is positive in the first and third quadrants. Since the reference angle is 6060 degrees, the angles that satisfy the equation in these quadrants are 6060 degrees and 180+60=240180 + 60 = 240 degrees.
  3. Determine Positive Quadrants: Write down the final answer with the angles found in Step 22.\newlineThe angles that satisfy the equation tan⁡(θ)=3\tan(\theta) = \sqrt{3} in the interval [0,360)[0, 360) degrees are 6060 degrees and 240240 degrees.

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