Solve in radians: tanθ=1.

To solve the equation tanθ=1 for θ in radians, follow these steps:

1. Recall that the tangent function, tan(θ), is equal to 1 at two places within the unit circle: π/4 and 5π/4. This is because tan(θ) is equal to sin(θ)/cos(θ), and both sin(θ) and cos(θ) are equal to √2/2 at these two angles, making their ratio 1.

2. Therefore, the solutions to the equation tanθ=1 within one period (0 to 2π) are θ = π/4 and θ = 5π/4.

3. However, the tangent function is periodic with a period of π. This means that any solution plus a multiple of π is also a solution.

4. Therefore, the general solutions to the equation tanθ=1 are θ = π/4 + nπ and θ = 5π/4 + nπ, where n is any integer.

To solve the equation tanθ=1 for θ in radians, follow these steps:

1. Recall that the tangent function, tan(θ), is equal to 1 at θ=π/4 and θ=5π/4 in the unit circle.

2. However, the tangent function is periodic with a period of π. This means that for any integer n, tan(θ) will also be 1 at θ=π/4 + nπ and θ=5π/4 + nπ.

3. Therefore, the general solutions to the equation tanθ=1 in radians are θ=π/4 + nπ and θ=5π/4 + nπ, where n is an integer.