교과서 질문
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
당신이 사용하는 게 아니라요?교과서 변경다른 교과서를 선택하세요
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, 9780135924891당신이 사용하는 게 아니라요?교과서 변경
4장, 문제 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°
검증된 단계별 안내1
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.
비슷한 문제에 대한 검증된 영상 답변:
이 영상 해법은 위 문제에 도움이 된다고 튜터들이 추천한 것입니다.
주요 개념
질문에 올바르게 답하기 위해 반드시 이해해야 하는 핵심 개념들은 다음과 같습니다.
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.
추천 영상:
가이드 코스
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.
추천 영상:
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.
추천 영상:
06:11Introduction to the Unit Circle
관련 실천
교과서 질문
Convert each degree measure to radians. If applicable, round to the nearest thousandth. See Example 1(c).
-47.69°
788
views
교과서 질문
Convert each radian measure to degrees. Write answers to the nearest minute. See Example 2(c).
2
846
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교과서 질문
Without using a calculator, decide whether each function value is positive or negative. (Hint: Consider the radian measures of the quadrantal angles, and remember that π ≈ 3.14.)
cos 2
803
views
교과서 질문
Without using a calculator, decide whether each function value is positive or negative. (Hint: Consider the radian measures of the quadrantal angles, and remember that π ≈ 3.14.)
sin ( ―1)
744
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교과서 질문
Work each problem. See Example 5. Angle Measure Find the measure (in radians) of a central angle of a sector of area 16 in² a circle of radius 3.0 in.
592
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