Domanda del libro di testo
Convert each degree measure to radians. If applicable, round to the nearest thousandth. See Example 1(c).
122° 37'
787
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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 55
Find the area of a sector of a circle having radius r and central angle θ. Express answers to the nearest tenth. See Example 5.
r = 40.0 mi, θ = 135°
Guida verificata passo dopo passo1
Recall the formula for the area of a sector of a circle: \(\text{Area} = \frac{\theta}{360^\circ} \times \pi r^2\), where \(\theta\) is the central angle in degrees and \(r\) is the radius of the circle.
Identify the given values: radius \(r = 40.0\) miles and central angle \(\theta = 135^\circ\).
Substitute the given values into the formula: \(\text{Area} = \frac{135}{360} \times \pi \times (40.0)^2\).
Simplify the fraction \(\frac{135}{360}\) by dividing numerator and denominator by their greatest common divisor to make calculations easier.
Calculate the numerical value of the area by multiplying the simplified fraction, \(\pi\), and the square of the radius, then round the result to the nearest tenth.
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Concetti chiave
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Area of a Sector
The area of a sector of a circle is the portion of the circle's area enclosed by two radii and the arc between them. It is calculated using the formula (θ/360) × π × r², where θ is the central angle in degrees and r is the radius. This formula helps find the fraction of the circle's area corresponding to the sector.
Video consigliato:
Percorso guidato
4:02
Calculating Area of SAS Triangles
Central Angle in Degrees
The central angle θ is the angle formed at the center of the circle by two radii. It determines the size of the sector. When given in degrees, it must be used directly in the sector area formula as a fraction of 360°, representing the full circle.
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Percorso guidato
04:46Coterminal Angles
Rounding and Units
After calculating the area, the result should be rounded to the nearest tenth to match the problem's requirement. Additionally, the units of the area will be the square of the radius units (e.g., square miles if radius is in miles), which is important for interpreting the final answer correctly.
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Percorso guidato
06:11Introduction to the Unit Circle
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