Solve for x tan(x)=-1/3

Problem

tan(x)=−1/3

Solution

1. Identify the general solution for the tangent function, which is x=arctan(k)+n*π for any integer n

2. Apply the inverse tangent to both sides of the equation to find the principal value.

x=arctan(−1/3)

3. Use the property of the arctangent function where arctan(−z)=−arctan(z)

x=−arctan(1/3)

4. Write the general solution by adding the period of the tangent function, which is π multiplied by an integer n

x=−arctan(1/3)+n*π

Final Answer

tan(x)=−1/3⇒x=−arctan(1/3)+n*π

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