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Ch. 5 - Trigonometric Identities
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. 5 - Trigonometric IdentitiesProblema 5.RE.26
Capitolo 6, Problema 5.RE.26

For each expression in Column I, use an identity to choose an expression from Column II with the same value. Choices may be used once, more than once, or not at all.
cos(-55°)

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1
Recall the even-odd identities for cosine and sine functions. Specifically, cosine is an even function, which means \(\cos(-\theta) = \cos(\theta)\) for any angle \(\theta\).
Apply this identity to the given expression: \(\cos(-55^\circ) = \cos(55^\circ)\).
Look at the expressions in Column II and find the one that matches \(\cos(55^\circ)\) exactly.
Confirm that the chosen expression from Column II is equivalent to \(\cos(-55^\circ)\) by using the even function property of cosine.
Select the matching expression from Column II as the equivalent expression for \(\cos(-55^\circ)\).

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Even-Odd Identities in Trigonometry

Even-odd identities describe how trigonometric functions behave with negative angles. Specifically, cosine is an even function, meaning cos(-θ) = cos(θ). This property allows simplification of expressions involving negative angles by converting them to positive angles.
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Even and Odd Identities

Cosine Function Properties

The cosine function measures the horizontal coordinate of a point on the unit circle and is periodic with period 360°. Understanding its symmetry and periodicity helps in simplifying and comparing trigonometric expressions, especially when angles are negative or exceed 360°.
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Graph of Sine and Cosine Function

Trigonometric Identities for Angle Transformations

Trigonometric identities, such as angle addition, subtraction, and negative angle identities, allow rewriting expressions in equivalent forms. These identities are essential tools for matching expressions from different forms by transforming angles or functions.
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Introduction to Transformations
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