Solve for x tan(x)=-4

Problem

tan(x)=−4

Solution

1. Identify the general solution for the tangent function. Since tan(x) has a period of π the general solution is x=arctan(a)+n*π where n is any integer.

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

x=arctan(−4)

3. Use the property of the arctangent function arctan(−x)=−arctan(x) to rewrite the expression.

x=−arctan(4)

4. Combine the principal value with the periodic property to express the general solution.

x=−arctan(4)+n*π

Final Answer

tan(x)=−4⇒x=−arctan(4)+n*π,n∈ℤ

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