Textbook Question
In Exercises 13β20, convert each angle in degrees to radians. Express your answer as a multiple of π.330Β°
550
views
1. Measuring Angles
Radians
2:34 minutesProblem 25
Textbook Question
In Exercises 21β28, convert each angle in radians to degrees.7π6
Verified step by step guidance1
Understand the relationship between radians and degrees: 180 degrees is equivalent to \( \pi \) radians.
To convert an angle from radians to degrees, use the formula: \( \text{Degrees} = \text{Radians} \times \frac{180}{\pi} \).
Substitute the given angle \( \frac{7\pi}{6} \) into the formula: \( \text{Degrees} = \frac{7\pi}{6} \times \frac{180}{\pi} \).
Simplify the expression by canceling out \( \pi \) from the numerator and denominator.
Multiply the remaining numbers to find the angle in degrees.
Verified video answer for a similar problem:This video solution was recommended by our tutors as helpful for the problem above
Video duration:
2mKey Concepts
Here are the essential concepts you must grasp in order to answer the question correctly.
Radians and Degrees
Radians and degrees are two units for measuring angles. A full circle is 360 degrees, which is equivalent to 2Ο radians. To convert between these units, one can use the relationship that 180 degrees equals Ο radians, allowing for straightforward calculations.
Recommended video:
5:04
Converting between Degrees & Radians
Conversion Formula
The conversion from radians to degrees can be performed using the formula: degrees = radians Γ (180/Ο). This formula provides a direct method to translate the measure of an angle from radians to degrees, ensuring accurate results in various applications.
Recommended video:
6:36Quadratic Formula
Simplifying Fractions
When converting angles, it is often necessary to simplify fractions. For example, when dealing with angles like 7Ο/6, recognizing that this can be expressed in terms of degrees helps in understanding the angle's position on the unit circle and its corresponding degree measure.
Recommended video:
4:02Solving Linear Equations with Fractions
Related Videos
Related Practice