Textbook Question
Find the length to three significant digits of each arc intercepted by a central angle in a circle of radius r. See Example 1.
r = 4.82 m , θ = 60°
Ch. 3 - Radian Measure and The Unit Circle
Lial12th EditionTrigonometryISBN: 9780136552161
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Table of contents
- 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
Chapter 4, Problem 17
Convert each degree measure to radians. Leave answers as multiples of π. See Examples 1(a) and 1(b). ―300°
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: \(-300^\circ \times \frac{\pi}{180}\).
Simplify the fraction \(\frac{-300}{180}\) by dividing numerator and denominator by their greatest common divisor.
Express the result as a multiple of \(\pi\), keeping the negative sign if applicable.
Write the final answer in the form \(\frac{a\pi}{b}\), where \(a\) and \(b\) are integers with no common factors.
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Key Concepts
Here are the essential concepts you must grasp in order to answer the question correctly.
Degree to Radian Conversion
Degrees and radians are two units for measuring angles. To convert degrees to radians, multiply the degree measure by π/180. This conversion is essential because radians are the standard unit in many trigonometric applications.
Recommended video:
5:04
Converting between Degrees & Radians
Understanding Negative Angles
Negative angles represent rotation in the clockwise direction. When converting negative degrees to radians, the sign is preserved, indicating the direction of rotation. This helps in correctly interpreting angle measures in trigonometry.
Recommended video:
04:46Coterminal Angles
Expressing Answers as Multiples of π
Leaving answers as multiples of π means writing the radian measure in the form (aπ/b), where a and b are integers. This exact form is preferred over decimal approximations to maintain precision and clarity in trigonometric expressions.
Recommended video:
6:36Simplifying Trig Expressions
Related Practice
Textbook Question
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s = ―π
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θ = 3.871 radians, t = 21.47 sec
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Textbook Question
Convert each radian measure to degrees.
-11π/18
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