Solve for b tan(b)=15/9

Problem

tan(b)=15/9

Solution

1. Simplify the fraction on the right side of the equation by dividing both the numerator and the denominator by their greatest common divisor, which is 3.

tan(b)=5/3

2. Apply the inverse tangent function to both sides of the equation to isolate the variable b

b=arctan(5/3)

3. Determine the general solution for b by accounting for the periodicity of the tangent function, which repeats every π radians.

b=arctan(5/3)+n*π

4. Calculate the approximate numerical value for the principal solution in radians and degrees if required.

b≈1.0304* radians

b≈59.04

Final Answer

b=arctan(5/3)+n*π

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