Domanda del libro di testo
Convert each radian measure to degrees. Write answers to the nearest minute. See Example 2(c).
9.84763
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Ch. 3 - Radian Measure and The Unit Circle
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 4, Problema 65
Find the approximate value of s, to four decimal places, in the interval [0 , π/2] that makes each statement true.
sec s = 1.0806
Guida verificata passo dopo passo1
Recall the definition of the secant function: \(\sec s = \frac{1}{\cos s}\). This means that \(\cos s = \frac{1}{\sec s}\).
Substitute the given value of \(\sec s\) into the equation: \(\cos s = \frac{1}{1.0806}\).
Calculate the value of \(\cos s\) from the above expression (you can do this with a calculator, but do not finalize the answer here).
Use the inverse cosine function to find \(s\): \(s = \arccos(\cos s)\), where \(s\) is in the interval \([0, \frac{\pi}{2}]\).
Express the value of \(s\) in radians and round it to four decimal places as required.
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Concetti chiave
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Definition of Secant Function
The secant function, sec(θ), is the reciprocal of the cosine function, defined as sec(θ) = 1/cos(θ). Understanding this relationship allows you to convert the given secant value into a cosine value, which is often easier to work with when solving for the angle.
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Percorso guidato
6:22
Graphs of Secant and Cosecant Functions
Inverse Trigonometric Functions
Inverse trigonometric functions, such as arccos, are used to find the angle corresponding to a given trigonometric value. After finding cos(s) from sec(s), applying arccos helps determine the angle s within the specified interval [0, π/2].
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Percorso guidato
4:28Introduction to Inverse Trig Functions
Domain and Range Restrictions
The problem restricts s to the interval [0, π/2], which corresponds to the first quadrant where cosine values are positive. This restriction ensures the solution is unique and helps in selecting the correct angle from the inverse cosine function.
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Percorso guidato
4:22Domain and Range of Function Transformations
Pratica correlata
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Find the approximate value of s, to four decimal places, in the interval [0, π/2] that makes each statement true.
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Domanda del libro di testo
Convert each radian measure to degrees. Write answers to the nearest minute. See Example 2(c).
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Find each exact function value. See Example 3.
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[π, 3π/2] ; tan s = √3
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