Final answer:
To find the value of u for tan(u) = -7/24 in the fourth quadrant, calculate the arctan(7/24) to get the reference angle, and subtract it from 2π. The tangent being negative indicates that u is in the fourth quadrant.
Step-by-step explanation:
To find the value of u when tan(u) = -7/24 and the angle u is in the fourth quadrant (since it is between 3π/2 and 2π), we first recognize that the tangent function is negative in the fourth quadrant. To find the angle whose tangent is -7/24, we use the inverse tangent function. However, since inverse tangent typically gives us an angle in the first or fourth quadrant, we specifically need the angle in the fourth quadrant, which we can find as 2π - |arctan(7/24)|.
The exact value of u in radians will be complicated and usually represented with the arctan function, but if you have the ability to calculate it, you would get an approximate decimal or degree value for u. Note that when using a calculator, you should ensure that it is set to the correct mode (radian or degree) to match your solution context.
To summarize, calculate the inverse tangent of 7/24 to find the reference angle, and subtract that angle from 2π to find the angle in the correct quadrant for u.