Find all angles, 0, degrees, is less than or equal to, theta, is less than, 360, degrees0 ∘ ≤θ<360 ∘ , that solve the following equation.tangent, theta, equals, minus, 1tanθ=−1
Question
Find all angles, 0, degrees, is less than or equal to, theta, is less than, 360, degrees0 ∘ ≤θ<360 ∘ , that solve the following equation.tangent, theta, equals, minus, 1tanθ=−1
Solution
The equation given is tan(θ) = -1.
The tangent function has a period of 180 degrees or π radians. This means that the function repeats its values every 180 degrees.
The tangent of an angle in the standard position is negative in the second and fourth quadrants.
In the second quadrant, the angle that has a tangent of -1 is 135 degrees (or 3π/4 radians).
In the fourth quadrant, the angle that has a tangent of -1 is 315 degrees (or 7π/4 radians).
So, the solutions to the equation tan(θ) = -1 in the interval 0 ≤ θ < 360 are θ = 135 degrees and θ = 315 degrees.
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