Textbook Question
Work each problem. See Example 5. Irrigation Area A center-pivot irrigation system provides water to a sector-shaped field as shown in the figure. Find the area of the field if θ = 40.0° and r = 152 yd.
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1. Measuring Angles
Radians
Problem 13
Textbook Question
Convert each degree measure to radians. Leave answers as multiples of π. See Examples 1(a) and 1(b). 90°
Verified step by step guidance1
Recall the formula to convert degrees to radians: \(\text{radians} = \text{degrees} \times \frac{\pi}{180}\).
Substitute the given degree measure into the formula: \(90^\circ \times \frac{\pi}{180}\).
Simplify the fraction \(\frac{90}{180}\) by dividing numerator and denominator by their greatest common divisor, which is 90.
After simplification, express the result as a multiple of \(\pi\).
Write the final answer in the form \(\frac{\pi}{2}\) radians.
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Key Concepts
Here are the essential concepts you must grasp in order to answer the question correctly.
Degree and Radian Measure
Degrees and radians are two units for measuring angles. A full circle is 360 degrees or 2π radians. Understanding the relationship between these units is essential for converting angles from degrees to radians.
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Converting between Degrees & Radians
Conversion Formula Between Degrees and Radians
To convert degrees to radians, multiply the degree measure by π/180. This formula comes from the fact that 180 degrees equals π radians, allowing a direct proportional conversion.
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Expressing Answers as Multiples of π
When converting to radians, answers are often left in terms of π to maintain exact values. This avoids decimal approximations and preserves the precision of the angle measurement.
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