Change 7/10 pi radians to degree measure
The Correct Answer and Explanation is:
To convert ( \frac{7}{10} \pi ) radians to degrees, you need to use the conversion factor between radians and degrees. The relationship between radians and degrees is based on the fact that a full circle is 360 degrees, which is equivalent to ( 2\pi ) radians. Therefore, to convert radians to degrees, the following formula is used:
[
\text{Degrees} = \text{Radians} \times \left(\frac{180^\circ}{\pi}\right)
]
Given the angle in radians is ( \frac{7}{10} \pi ), the conversion to degrees is:
[
\text{Degrees} = \frac{7}{10} \pi \times \left(\frac{180^\circ}{\pi}\right)
]
Now, cancel out ( \pi ) from both the numerator and denominator:
[
\text{Degrees} = \frac{7}{10} \times 180^\circ
]
Next, multiply ( \frac{7}{10} ) by 180:
[
\text{Degrees} = \frac{7 \times 180}{10} = \frac{1260}{10} = 126^\circ
]
Thus, ( \frac{7}{10} \pi ) radians is equal to ( 126^\circ ).
Explanation:
In this calculation, we started with the known relationship between radians and degrees, ( 2\pi ) radians being equivalent to 360 degrees. By multiplying the given radian measure by ( \frac{180^\circ}{\pi} ), we apply this conversion factor to the expression for radians. This allows us to convert from the circular measure in radians to the angular measure in degrees.
This process highlights a fundamental aspect of working with angles: knowing how to convert between different units of angular measurement is essential for solving problems in trigonometry and other areas of mathematics. Whether working with radians or degrees, both systems are used to describe the same quantity but in different units. Understanding how to convert between them ensures flexibility in problem-solving and enhances the ability to work with angles in various contexts.