Solve for x tan(x)=-4/3

Problem

tan(x)=−4/3

Solution

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

2. Calculate the principal value using the inverse tangent function.

x=arctan(−4/3)

3. Determine the numerical value if needed. Using a calculator, the principal value is approximately −0.927 radians or −53.13^∘

4. Express the general solution by adding the periodic constant n*π

x=arctan(−4/3)+n*π

Final Answer

tan(x)=−4/3⇒x=arctan(−4/3)+n*π

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