Textbook Question
In Exercises 21–28, convert each angle in radians to degrees.7𝜋6
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1. Measuring Angles
Radians
2:23 minutesProblem 35
Textbook Question
In Exercises 35–40, convert each angle in radians to degrees. Round to two decimal places.2 radians
Verified step by step guidance1
insert step 1> Start by recalling the conversion factor between radians and degrees: $1 ext{ radian} = \frac{180}{\pi} ext{ degrees}$.
insert step 2> Multiply the given angle in radians by the conversion factor to convert it to degrees: $2 ext{ radians} \times \frac{180}{\pi}$.
insert step 3> Simplify the expression by multiplying the numbers: $2 \times 180 = 360$.
insert step 4> Divide the result by $\pi$: $\frac{360}{\pi}$.
insert step 5> Round the result to two decimal places to get the final answer in degrees.
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Key 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 2π radians. This means that to convert between these units, one can use the relationship that 180 degrees equals π radians.
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Conversion Formula
To convert radians to degrees, the formula is: degrees = radians × (180/π). This formula allows for the straightforward conversion of any angle measured in radians to its equivalent in degrees, facilitating easier interpretation and application in various contexts.
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Rounding Numbers
Rounding is the process of adjusting a number to a specified degree of accuracy. In this case, rounding to two decimal places means keeping two digits after the decimal point. This is important for clarity and precision in reporting measurements, especially in mathematical contexts.
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