Domanda del libro di testo
Convert each radian measure to degrees. Write answers to the nearest minute. See Example 2(c).
3.06
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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 61
Find the approximate value of s, to four decimal places, in the interval [0, π/2] that makes each statement true.
tan s = 0.2126
Guida verificata passo dopo passo1
Identify the given equation: \(\tan s = 0.2126\), where \(s\) is in the interval \([0, \frac{\pi}{2}]\).
Recall that to find \(s\), you need to use the inverse tangent function (also called arctangent), which is written as \(\arctan\) or \(\tan^{-1}\).
Apply the inverse tangent to both sides of the equation to isolate \(s\): \(s = \arctan(0.2126)\).
Use a calculator set to radians mode to find the approximate value of \(s\) by evaluating \(\arctan(0.2126)\).
Round the result to four decimal places to get the final approximate value of \(s\) within the interval \([0, \frac{\pi}{2}]\).
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Concetti chiave
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Understanding the Tangent Function
The tangent function relates an angle in a right triangle to the ratio of the opposite side over the adjacent side. It is periodic and defined for all angles except where cosine is zero. Knowing how to interpret tan s = 0.2126 helps in finding the angle s whose tangent value matches this ratio.
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5:43
Introduction to Tangent Graph
Inverse Tangent (Arctan) Function
The inverse tangent function, denoted arctan or tan⁻¹, is used to find the angle whose tangent is a given number. Since tan s = 0.2126, s = arctan(0.2126) gives the angle in radians. This function returns values typically in the interval (-π/2, π/2), which includes the given domain [0, π/2].
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3:17Inverse Tangent
Radian Measure and Interval Constraints
Angles can be measured in radians, where π radians equal 180 degrees. The problem restricts s to the interval [0, π/2], meaning s is between 0 and 90 degrees. Understanding this interval ensures the correct solution is chosen, especially since tangent is positive and increasing in this range.
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5:04Converting between Degrees & Radians
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Convert each radian measure to degrees. Write answers to the nearest minute. See Example 2(c).
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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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