Find all angles, 0, degrees, is less than or equal to, theta, is less than, 360, degrees0 ∘ ≤θ<360 ∘ , that satisfy the equation below, to the nearest tenth of a degree (if necessary).minus, tangent, theta, plus, 2, equals, 4, tangent, theta, plus, 7−tanθ+2=4tanθ+7
Question
Find all angles, 0, degrees, is less than or equal to, theta, is less than, 360, degrees0 ∘ ≤θ<360 ∘ , that satisfy the equation below, to the nearest tenth of a degree (if necessary).minus, tangent, theta, plus, 2, equals, 4, tangent, theta, plus, 7−tanθ+2=4tanθ+7
Solution
The given equation is -tanθ + 2 = 4tanθ + 7.
First, let's rearrange the equation to isolate tanθ.
This gives us 5tanθ = -5, or tanθ = -1.
The angles that satisfy this equation are θ = 135° and θ = 315° in the range 0° ≤ θ < 360°.
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