Domanda del libro di testo
Convert each degree measure to radians. Leave answers as multiples of π. See Examples 1(a) and 1(b). ―315°
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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 17
Find the length to three significant digits of each arc intercepted by a central angle in a circle of radius r. See Example 1.
r = 4.82 m , θ = 60°
Guida verificata passo dopo passo1
Recall the formula for the length of an arc intercepted by a central angle in a circle: \(\text{Arc length} = r \times \theta\), where \(r\) is the radius and \(\theta\) is the central angle in radians.
Since the given angle \(\theta\) is in degrees, convert it to radians using the conversion formula: \(\theta_{\text{radians}} = \theta_{\text{degrees}} \times \frac{\pi}{180}\).
Substitute the given values into the conversion formula: \(\theta_{\text{radians}} = 60 \times \frac{\pi}{180}\).
Calculate the arc length by multiplying the radius \(r = 4.82\) m by the angle in radians: \(\text{Arc length} = 4.82 \times \theta_{\text{radians}}\).
Express the final answer rounded to three significant digits as required.
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Arc Length Formula
The arc length of a circle segment is calculated using the formula s = rθ, where r is the radius and θ is the central angle in radians. This formula relates the linear distance along the circle's edge to the angle subtended at the center.
Video consigliato:
Percorso guidato
4:18
Finding Missing Side Lengths
Conversion Between Degrees and Radians
Since the arc length formula requires the angle in radians, converting degrees to radians is essential. Use the conversion factor π radians = 180°, so θ (radians) = θ (degrees) × π / 180.
Video consigliato:
Percorso guidato
5:04Converting between Degrees & Radians
Significant Figures in Measurement
When reporting the arc length, it is important to round the result to three significant digits to reflect the precision of the given data. This ensures the answer is both accurate and appropriately precise.
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Percorso guidato
8:22Example 2
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