Textbook Question
Find the length of the arc on a circle of radius 20 feet intercepted by a 75° central angle. Express arc length in terms of 𝜋. Then round your answer to two decimal places.
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1. Measuring Angles
Radians
2:00 minutesProblem 14
Textbook Question
In Exercises 13–20, convert each angle in degrees to radians. Express your answer as a multiple of 𝜋.18°
Verified step by step guidance1
Start with the formula to convert degrees to radians: \( \text{radians} = \text{degrees} \times \frac{\pi}{180} \).
Substitute the given angle in degrees into the formula: \( 18° \times \frac{\pi}{180} \).
Simplify the fraction by dividing both the numerator and the denominator by their greatest common divisor.
The simplified fraction will give you the angle in radians as a multiple of \( \pi \).
Express the final result as a simplified fraction multiplied by \( \pi \).
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Video duration:
2mKey Concepts
Here are the essential concepts you must grasp in order to answer the question correctly.
Degrees and Radians
Degrees and radians are two units for measuring angles. A full circle is 360 degrees, which is equivalent to 2π radians. Understanding the relationship between these two units is essential for converting angles from one to the other.
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5:04
Converting between Degrees & Radians
Conversion Formula
To convert an angle from degrees to radians, you can use the formula: radians = degrees × (π/180). This formula allows you to express the angle in radians as a multiple of π, which is often required in trigonometric contexts.
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Multiples of π
Expressing angles in terms of multiples of π is common in trigonometry. For example, an angle of 18° converted to radians would be expressed as a fraction of π, making it easier to work with in equations and functions that involve trigonometric ratios.
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