Solve for y 4pi+4arctan(y)=pi

Problem

4*π+4*arctan(y)=π

Solution

1. Isolate the term containing the inverse tangent by subtracting 4*π from both sides of the equation.

4*arctan(y)=π−4*π

4*arctan(y)=−3*π

2. Divide both sides by 4 to solve for the arctan(y) expression.

arctan(y)=−(3*π)/4

3. Apply the tangent function to both sides to eliminate the inverse tangent and solve for y

y=tan(−(3*π)/4)

4. Evaluate the tangent value using the unit circle or the property that tan(−x)=−tan(x)

y=−tan((3*π)/4)

y=−(−1)

y=1

Final Answer

y=1

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