Domanda del libro di testo
Determine whether each statement is possible or impossible. See Example 4. cot θ = ―6
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Ch. 1 - Trigonometric Functions
Lial12th EditionTrigonometryISBN: 9780136552161, 9780135440780, 9780136881117, 9780135440827, 9780135924891
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TOC.tableOfContents
- Ch. R - Algebra Review381
- Ch. 1 - Trigonometric Functions188
- Ch. 2 - Acute Angles and Right Triangles168
- Ch. 3 - Radian Measure and The Unit Circle155
- Ch. 4 - Graphs of the Circular Functions100
- Ch. 5 - Trigonometric Identities238
- Ch. 6 - Inverse Circular Functions and Trigonometric Equations158
- Ch. 7 - Applications of Trigonometry and Vectors148
- Ch. 8 - Complex Numbers, Polar Equations, and Parametric Equations15
Lial12th EditionTrigonometryISBN: 9780136552161, 9780135440780, 9780136881117, 9780135440827, 9780135924891Non è quello che usi tu?Cambia libro di testo
Capitolo 2, Problema 67
Find the indicated function value. If it is undefined, say so. See Example 4. sec 180°
Guida verificata passo dopo passo1
Recall the definition of the secant function: \(\sec \theta = \frac{1}{\cos \theta}\).
Identify the angle given: \(180^\circ\).
Find the cosine of \(180^\circ\): \(\cos 180^\circ\).
Evaluate \(\cos 180^\circ\) using the unit circle or known values. (Note: \(\cos 180^\circ = -1\).)
Calculate \(\sec 180^\circ\) by taking the reciprocal of \(\cos 180^\circ\), i.e., \(\sec 180^\circ = \frac{1}{\cos 180^\circ}\).
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Definition of the Secant Function
The secant function, sec(θ), is the reciprocal of the cosine function: sec(θ) = 1/cos(θ). It is defined wherever cosine is not zero. Understanding this reciprocal relationship is essential to evaluate secant values for given angles.
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Percorso guidato
6:22
Graphs of Secant and Cosecant Functions
Cosine of Special Angles
Cosine values for special angles like 0°, 90°, 180°, and 270° are fundamental. For 180°, cos(180°) = -1. Knowing these values helps directly compute sec(180°) by taking the reciprocal of cosine at that angle.
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Percorso guidato
4:35Intro to Law of Cosines
Domain and Undefined Values of Trigonometric Functions
Trigonometric functions can be undefined when their denominators are zero. Since sec(θ) = 1/cos(θ), sec(θ) is undefined where cos(θ) = 0. Recognizing these points prevents errors in evaluation and helps identify when a function value does not exist.
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Percorso guidato
4:22Domain and Range of Function Transformations
Pratica correlata
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Convert each angle measure to degrees, minutes, and seconds. If applicable, round to the nearest second. See Example 4(b). 174.255°
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Domanda del libro di testo
Use identities to solve each of the following. Rationalize denominators when applicable. See Examples 5–7. Find csc θ , given that cot θ = ―1/2 and θ is in quadrant IV.
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Find the indicated function value. If it is undefined, say so. See Example 4. sin 90°
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