Textbook Question
In Exercises 7–12, find the radian measure of the central angle of a circle of radius r that intercepts an arc of length s. Radius, r: 10 inches Arc Length, s: 40 inches
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1. Measuring Angles
Radians
2:11 minutesProblem 16
Textbook Question
In Exercises 13–20, convert each angle in degrees to radians. Express your answer as a multiple of 𝜋.150°
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 (150°) into the formula: \( 150 \times \frac{\pi}{180} \).
Simplify the fraction \( \frac{150}{180} \) by dividing both the numerator and the denominator by their greatest common divisor, which is 30.
This simplification gives \( \frac{5}{6} \).
Therefore, the angle in radians is \( \frac{5\pi}{6} \).
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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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Converting between Degrees & Radians
Conversion Formula
To convert degrees to radians, the formula used is: radians = degrees × (π/180). This formula allows for the direct conversion of any angle measured in degrees into its corresponding value in radians.
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Multiples of π
When expressing angles in radians, it is common to represent them as multiples of π. This means that the radian measure is expressed in terms of π, such as nπ, where n is a rational number. This format is particularly useful in trigonometry for simplifying expressions and solving equations.
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