Domanda del libro di testo
Give all six trigonometric function values for each angle θ. Rationalize denominators when applicable. See Examples 5–7.
csc θ = ―3 , and cos θ > 0
685
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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 79
Find the indicated function value. If it is undefined, say so. See Example 4. sec 1800°
Guida verificata passo dopo passo1
Recall that the secant function is the reciprocal of the cosine function, so \(\sec \theta = \frac{1}{\cos \theta}\).
Since the angle given is \(1800^\circ\), reduce it to an equivalent angle between \(0^\circ\) and \(360^\circ\) by subtracting multiples of \(360^\circ\): calculate \(1800^\circ - 5 \times 360^\circ\).
Simplify the expression to find the equivalent angle: \(1800^\circ - 1800^\circ = 0^\circ\).
Evaluate \(\cos 0^\circ\), knowing that \(\cos 0^\circ = 1\).
Find \(\sec 1800^\circ\) by taking the reciprocal of \(\cos 0^\circ\), so \(\sec 1800^\circ = \frac{1}{1}\).
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Understanding the Secant Function
The secant function, sec(θ), is the reciprocal of the cosine function, defined as sec(θ) = 1/cos(θ). It is undefined wherever cos(θ) equals zero, which occurs at odd multiples of 90°. Knowing this helps determine when sec(θ) is defined or undefined.
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Percorso guidato
6:22
Graphs of Secant and Cosecant Functions
Angle Coterminality and Reduction
Angles differing by full rotations (360°) share the same trigonometric values. To simplify large angles like 1800°, subtract multiples of 360° to find a coterminal angle between 0° and 360°, making it easier to evaluate the function.
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Percorso guidato
04:46Coterminal Angles
Evaluating Trigonometric Functions at Standard Angles
Trigonometric functions have known values at standard angles such as 0°, 90°, 180°, and 270°. Recognizing these values allows quick evaluation of functions like sec(θ) once the angle is reduced, facilitating identification of defined or undefined values.
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Percorso guidato
05:50Drawing Angles in Standard Position
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Give all six trigonometric function values for each angle θ. Rationalize denominators when applicable. See Examples 5–7.
sin θ = √2/6 , and cos θ < 0
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Domanda del libro di testo
Find the indicated function value. If it is undefined, say so. See Example 4. cos 1800°
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Give all six trigonometric function values for each angle θ. Rationalize denominators when applicable. See Examples 5–7.
cos θ = 1
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