Solve for x tan(x)=-3

Problem

tan(x)=−3

Solution

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

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

x=arctan(−3)

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

x=−arctan(3)

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

x=−arctan(3)+n*π

Final Answer

tan(x)=−3⇒x=−arctan(3)+n*π

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