Explanation:
To find the coterminal angle with -442° we can add or subtract any integer multiple of 360°.
-442° + 360° = -82°
So one coterminal angle with -442° is -82°.
To determine the quadrant, we need to consider the sign of the angles in each quadrant. Since -442° is negative, it lies in the clockwise direction, which means it falls in the fourth quadrant.
To find the reference angle, we need to find the acute angle between the terminal side of the angle and the x-axis. We can do that by subtracting the nearest multiple of 360°.
-442° + 360° = -82° (the smallest positive coterminal angle)
Reference angle = 82°
Therefore, the coterminal angle with -442° between 0° and 360° is 318°, it lies in the fourth quadrant and the reference angle is 82°.