Final answer:
To find a co-terminal angle, add or subtract full rotations (360° or 2π) to/from the initial angle. For a reference angle, use the acute angle made with the closest x-axis by subtracting the angle from the nearest multiple of 180° or π.
Step-by-step explanation:
To find a co-terminal angle in mathematics, you can add or subtract multiples of 360° (for angles measured in degrees) or 2π (for angles measured in radians) to the original angle. The co-terminal angles are angles that have the same initial and terminal sides as the original angle but may have been rotated several full turns more or less. To find a reference angle for an angle in standard position, you measure the acute angle it makes with the closest x-axis. This is typically done by finding the absolute value of the original angle minus the nearest multiple of 180° if working in degrees, or π if working in radians.A reference angle is always between 0 and 90 degrees (0 and π/2 radians), so once you have the absolute value, if it is not already acute, then subtract it from 180° or π to get the acute reference angle. Remember, that co-terminal angles and reference angles are used to simplify trigonometric calculations and to understand the properties of angles in different quadrants of the coordinate plane.