Final answer:
The coterminal angle for -58° is 302°. It lies in the fourth quadrant and has a reference angle of 58°.
Step-by-step explanation:
To find the coterminal angle for a given rotation of -58°, we can add or subtract multiples of 360° until we get an angle between 0° and 360°.
Coterminal angles are angles that have the same initial and terminal sides but differ by a multiple of 360°.
In this case, we can add 360° to -58° to get the coterminal angle.
-58° + 360°
= 302°.
The quadrant for the coterminal angle 302° would be the fourth quadrant since it lies between 270° and 360°.
The reference angle is the acute angle formed between the terminal side of the given angle and the x-axis.
For the angle 302°, the reference angle would be 58° (obtained by subtracting 360° - 302°).