Final answer:
The expression sin(-7 √ 58/58) simplifies to sin(-7), which strictly doesn't match any of the multiple-choice options. Given the options, the closest by approximation would be -30°, though this is not an exact match and assumes a potential typographical error in the question.
Step-by-step explanation:
The student is asking to find the degree measure for the expression sin(-7 √ 58/58). To answer this, we need to simplify the expression inside the sine function first. Since √ 58/58 is equal to √ 1, which in turn equals 1, the original expression simplifies to sin(-7). Now, -7 degrees is the measure of the angle in standard position, but sine is generally defined in terms of right triangles with acute angles, or else by the unit circle where the angle is considered in radians. However, for the sake of answering the multiple-choice question, we need to find which of the options given is closest to -7 degrees, knowing the typical acute angles associated with basic sine values.
Since none of the given options exactly match -7 degrees, and knowing that sine can be positive or negative depending on the quadrant the angle lies in, we can consider the acute angle reference of -7 degrees, which is 7 degrees. In basic trigonometric functions, none of the provided options A) -75°, B) -60°, C) -45°, D) -30° are directly equivalent to this. However, if there is any typographical error in the question, based on the basic knowledge of trigonometry, the closest would technically be -30°, since its sine value is -1/2, and 7 degrees creates a small sine value. Hence, one could argue that option D) -30° seems the most plausible answer, though it's a rough approximation and assumes there's an error in the problem presentation.