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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 76
Capitolo 2, Problema 76

Find the indicated function value. If it is undefined, say so. See Example 4. cos 1800°

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1
Recognize that the cosine function is periodic with a period of 360°, meaning that \(\cos(\theta) = \cos(\theta + 360°k)\) for any integer \(k\).
To simplify \(\cos 1800°\), reduce the angle by subtracting multiples of 360° until the angle lies within the standard range of \$0°$ to \$360°$. Calculate \(1800° - 360° \times k\) where $k$ is chosen so the result is between \$0°$ and \$360°$.
Perform the calculation: \(1800° - 360° \times 5 = 1800° - 1800° = 0°\). So, \(\cos 1800° = \cos 0°\).
Recall the value of \(\cos 0°\), which is a fundamental trigonometric value.
Conclude that \(\cos 1800°\) is equal to \(\cos 0°\) and state the corresponding cosine value.

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Angle Measurement and Coterminal Angles

Angles can be measured in degrees and can exceed 360°, representing multiple rotations. Coterminal angles differ by full rotations of 360° and share the same trigonometric values. To find the value of a function at a large angle, reduce it by subtracting multiples of 360° to find an equivalent angle within 0° to 360°.
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Coterminal Angles

Cosine Function Properties

The cosine function relates an angle to the x-coordinate of a point on the unit circle. It is periodic with a period of 360°, meaning cos(θ) = cos(θ + 360°k) for any integer k. Cosine values range between -1 and 1 and are defined for all real angles.
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Graph of Sine and Cosine Function

Evaluating Trigonometric Functions at Specific Angles

To evaluate cos 1800°, first find the coterminal angle by subtracting multiples of 360°. For example, 1800° - 5×360° = 0°, so cos 1800° = cos 0° = 1. This method simplifies calculations and helps determine if the function value is defined or undefined.
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Evaluate Composite Functions - Special Cases
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Find the indicated function value. If it is undefined, say so. See Example 4. sec 1800°

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