Find the angle of least positive measure (not equal to the given measure) that is coterminal with each angle. See Example 5. 8440°

Verified step by step guidance

Step 1: Understand that 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°.

Step 2: Start with the given angle, 8440°, and determine how many full rotations (360°) are contained within it. This is done by dividing 8440° by 360°.

Step 3: Calculate the remainder when 8440° is divided by 360°. This remainder will give you the angle of least positive measure that is coterminal with 8440°.

Step 4: If the remainder is 0, it means the angle is already a multiple of 360°, and you should subtract 360° to find the least positive coterminal angle.

Step 5: The result from Step 3 or Step 4 is the angle of least positive measure that is coterminal with 8440°.

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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, differing by full rotations of 360 degrees. To find a coterminal angle, you can add or subtract multiples of 360° from the given angle. For example, 8440° can be reduced by subtracting 360° repeatedly until the angle falls within the range of 0° to 360°.

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. This is typically found by reducing the angle to its equivalent within the first full rotation (0° to 360°). If the angle is already positive, the least positive angle is simply the result of the coterminal angle calculation.

Modulo Operation

The modulo operation is a mathematical operation that finds the remainder when one number is divided by another. In the context of angles, using modulo 360° helps to determine the equivalent angle within a single rotation. For instance, calculating 8440° mod 360° gives the least positive angle coterminal with 8440°, simplifying the process of finding angles in trigonometry.

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