Solve the given equation. (Enter your answers as a comma-separated list. Let k be any integer. Round terms to two decimal places where appropriate.)
tan θ = 1
To solve the equation tan θ = 1, we need to find the values of θ that satisfy this equation.
The tangent function is positive in two quadrants: the first quadrant (0 < θ < 90 degrees) and the third quadrant (180 < θ < 270 degrees).
In the first quadrant, the tangent function is equal to the ratio of the opposite side to the adjacent side of a right triangle. When this ratio is 1, it means the opposite side and the adjacent side are equal in length, which forms a 45-degree angle (π/4 radians).
In the third quadrant, the tangent function is also equal to the ratio of the opposite side to the adjacent side of a right triangle. Again, when this ratio is 1, it means the opposite side and the adjacent side are equal in length, forming a 45-degree angle (π/4 radians). However, in the third quadrant, the tangent function is negative.
Therefore, the solutions for the equation tan θ = 1 are θ = π/4 + kπ and θ = 3π/4 + kπ, where k is any integer.
To express these solutions as degree measures, you can convert radians to degrees using the formula: degrees = (radians * 180) / π.
So, the rounded degree solutions for the equation tan θ = 1 are θ = 45 + 180k degrees and θ = 135 + 180k degrees, where k is any integer.