Solve for x tan(x)=-1

Problem

tan(x)=−1

Solution

1. Identify the reference angle by finding the value of θ such that tan(θ)=1 In the first quadrant, θ=π/4

2. Determine the quadrants where the tangent function is negative. Tangent is negative in the second and fourth quadrants.

3. Calculate the specific angles within the interval [0,2*π) by applying the reference angle to the identified quadrants.

4. Apply the second quadrant formula: x=π−π/4=(3*π)/4

5. Apply the fourth quadrant formula: x=2*π−π/4=(7*π)/4

6. Generalize the solution because the tangent function has a period of π The solutions can be expressed by adding integer multiples of the period to the primary solution.

Final Answer

x=(3*π)/4+n*π

Want more problems? Check here!