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Ch. 3 - Radian Measure and The Unit Circle
Lial - Trigonometry 12th Edition
Lial12th EditionTrigonometryISBN: 9780136552161, 9780135440780, 9780136881117, 9780135440827, 9780135924891Non è quello che usi tu?Cambia libro di testo
Tutti i libri di testoLial 12th EditionCh. 3 - Radian Measure and The Unit CircleProblema 51
Capitolo 4, Problema 51

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 = 30.0 ft, θ = π/2 radians

Guida verificata passo dopo passo
1
Recall the formula for the area of a sector of a circle: \(\text{Area} = \frac{1}{2} r^{2} \theta\), where \(r\) is the radius and \(\theta\) is the central angle in radians.
Identify the given values: radius \(r = 30.0\) ft and central angle \(\theta = \frac{\pi}{2}\) radians.
Substitute the given values into the formula: \(\text{Area} = \frac{1}{2} \times (30.0)^{2} \times \frac{\pi}{2}\).
Simplify the expression step-by-step: first square the radius, then multiply by \(\frac{1}{2}\) and \(\frac{\pi}{2}\).
After simplifying, calculate the numerical value and round your answer to the nearest tenth to find the area of the sector.

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Area of a Sector

The area of a sector of a circle is a portion of the circle's total area, determined by the central angle. It is calculated using the formula A = (1/2) * r² * θ, where r is the radius and θ is the central angle in radians. This formula directly relates the angle to the fraction of the circle's area.
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Calculating Area of SAS Triangles

Radian Measure

Radians measure angles based on the radius of a circle, where one radian is the angle subtended by an arc equal in length to the radius. Using radians simplifies many trigonometric formulas, including the sector area formula, because it relates angle measure directly to arc length and area.
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Rounding and Approximation

After calculating the area, results often need to be rounded to a specified precision, such as the nearest tenth. This involves understanding decimal places and applying standard rounding rules to present the answer clearly and accurately, especially in practical contexts like measurements.
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