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Ch. 1 - Trigonometric Functions
Lial - Trigonometry 12th Edition
Lial12th EditionTrigonometryISBN: 9780136552161, 9780135440780, 9780136881117, 9780135440827, 9780135924891Non è quello che usi tu?Cambia libro di testo
Tutti i libri di testoLial 12th EditionCh. 1 - Trigonometric FunctionsProblema 92
Capitolo 2, Problema 92

Find the angle of least positive measure (not equal to the given measure) that is coterminal with each angle. 1000°

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1
Understand that angles are coterminal if they differ by a full rotation of 360°. This means we can add or subtract multiples of 360° to find coterminal angles.
Since the given angle is 1000°, to find a coterminal angle with the least positive measure (other than 1000° itself), subtract multiples of 360° until the result is between 0° and 360°.
Set up the expression: \(1000° - 360° \times n\), where \(n\) is an integer chosen so that the result lies in the interval \((0°, 360°)\).
Calculate the appropriate value of \(n\) by dividing 1000 by 360 and taking the integer part: \(n = \lfloor \frac{1000}{360} \rfloor\).
Subtract \(360° \times n\) from 1000° to find the coterminal angle with the least positive measure different from 1000°.

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Coterminal Angles

Coterminal angles are angles that share the same initial and terminal sides but differ by full rotations of 360°. To find coterminal angles, you add or subtract multiples of 360° from the given angle. This concept helps identify angles that represent the same direction in standard position.
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Coterminal Angles

Angle Measurement and Positive Angles

Angles can be measured in degrees, and positive angles are measured counterclockwise from the positive x-axis. The least positive coterminal angle is the smallest positive angle greater than 0° that is coterminal with the given angle, ensuring it is not equal to the original angle.
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Drawing Angles in Standard Position

Modulo Operation in Angle Reduction

Finding the least positive coterminal angle involves using the modulo operation with 360°, which effectively reduces any angle to its equivalent between 0° and 360°. This operation simplifies large angles by removing full rotations, making it easier to identify the smallest positive coterminal angle.
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Algebraic Operations on Vectors
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