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

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insert step 1> Convert the given angle from degrees to a standard position by finding its coterminal angle.

insert step 2> To find a coterminal angle, add or subtract multiples of 360° from the given angle.

insert step 3> Subtract 360° from 541° to find a positive coterminal angle less than 541°.

insert step 4> Check if the resulting angle is positive and less than 360°. If not, continue subtracting 360° until it is.

insert step 5> The resulting angle is the least positive coterminal angle with the given angle.

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

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.

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