Find the angle of least positive measure (not equal to the given measure) that is coterminal with each angle. See Example 5. 541°

Verified step by step guidance

1. <insert step 1> Convert the given angle from degrees to a standard position by finding its coterminal angle.>
2. <insert step 2> To find a coterminal angle, add or subtract multiples of 360° from the given angle.>
3. <insert step 3> Subtract 360° from 541° to find a positive coterminal angle less than 541°.>
4. <insert step 4> Check if the resulting angle is positive and less than 360°. If not, continue subtracting 360° until it is.>
5. <insert step 5> The resulting angle is the least positive coterminal angle with the given angle.>

Key Concepts

Coterminal Angles

Coterminal angles are angles that share the same terminal side when drawn in standard position. To find a coterminal angle, you can add or subtract multiples of 360° (for degrees) or 2π (for radians) from the given angle. For example, 541° can be made coterminal by subtracting 360°, resulting in 181°.

Finding the Least Positive Angle

The least positive angle coterminal with a given angle is the smallest angle greater than zero that shares the same terminal side. To find this angle, you can repeatedly subtract 360° from the original angle until the result is within the range of 0° to 360°. This ensures that the angle is positive and not equal to the original angle.

Angle Measurement

Angles can be measured in degrees or radians, with 360° equivalent to 2π radians. Understanding how to convert between these two systems is essential for solving problems involving angles. In this context, knowing that 541° exceeds 360° helps in determining the appropriate coterminal angle by reducing it to a standard range.