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CONCEPT PREVIEW Find the area of each sector.
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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 7
CONCEPT PREVIEW Find the area of each sector.
Guida verificata passo dopo passo1
Identify the given information for the sector: the radius \(r\) of the circle and the central angle \(\theta\) of the sector. The angle should be in degrees or radians.
Recall the formula for the area of a sector: \(\text{Area} = \frac{\theta}{360} \times \pi r^{2}\) if \(\theta\) is in degrees, or \(\text{Area} = \frac{1}{2} r^{2} \theta\) if \(\theta\) is in radians.
If the angle \(\theta\) is given in degrees, use the first formula. If it is in radians, use the second formula. Convert the angle to the appropriate unit if necessary.
Substitute the values of \(r\) and \(\theta\) into the chosen formula to set up the expression for the area of the sector.
Simplify the expression to find the area of the sector (do not calculate the final numeric value unless asked).
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Concetti chiave
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Definition of a Sector
A sector is a portion of a circle enclosed by two radii and the arc between them. Understanding what constitutes a sector helps in visualizing the problem and identifying the relevant parts of the circle needed to calculate the area.
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Percorso guidato
04:26
Parameterizing Equations Example 1
Formula for the Area of a Sector
The area of a sector is given by (θ/360) × πr², where θ is the central angle in degrees and r is the radius of the circle. This formula relates the fraction of the circle represented by the sector to the total area of the circle.
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Percorso guidato
4:30Calculating Area of ASA Triangles
Conversion Between Radians and Degrees
Since angles can be given in radians or degrees, knowing how to convert between these units (1 radian = 180/π degrees) is essential. This ensures the correct application of the area formula depending on the angle's unit.
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Percorso guidato
5:04Converting between Degrees & Radians
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