Textbook Question
In Exercises 59–62, use a calculator to find the value of the acute angle θ in radians, rounded to three decimal places.tan θ = 0.4169
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1. Measuring Angles
Angles in Standard Position
1:05 minutesProblem 6
Textbook Question
CONCEPT PREVIEW Fill in the blank to correctly complete each sentence. One minute, written 1' , is ________________ of a degree.
Verified step by step guidance1
Understand that a degree is a unit of measurement for angles, commonly used in geometry and trigonometry.
Recognize that a degree can be further divided into smaller units for more precise measurements.
Recall that one degree is divided into 60 equal parts, known as minutes.
Therefore, one minute, written as 1', is 1/60 of a degree.
This division allows for more precise angle measurements, especially in fields like astronomy and navigation.
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Key Concepts
Here are the essential concepts you must grasp in order to answer the question correctly.
Degrees and Minutes
In trigonometry, angles are often measured in degrees, where one full rotation is 360 degrees. A minute is a subdivision of a degree, specifically, one degree is divided into 60 minutes. This means that 1 minute is equal to 1/60th of a degree, which is crucial for precise angle measurements in various applications.
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Conversion between Units
Understanding how to convert between different units of measurement is essential in trigonometry. In this context, converting minutes to degrees involves recognizing that 1 minute equals 1/60 of a degree. This conversion is fundamental when working with angles in calculations, ensuring accuracy in trigonometric functions.
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Trigonometric Functions
Trigonometric functions, such as sine, cosine, and tangent, are based on angles measured in degrees or radians. Knowing how to express angles in different units, including degrees and minutes, is vital for applying these functions correctly. This understanding allows for effective problem-solving in trigonometry, especially when dealing with real-world applications.
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