Convert 7π/10 from radians to degrees.

Convert 7π/10 from radians to degrees.

The Correct Answer and Explanation is:

To convert an angle from radians to degrees, we use the relationship between these two units of measurement. The fundamental conversion factor is that (180^\circ) is equivalent to (\pi) radians. Therefore, to convert radians to degrees, we can multiply the radian measure by (\frac{180^\circ}{\pi}).

In this case, we have the angle ( \frac{7\pi}{10} ) radians that we want to convert to degrees. Here are the steps involved in the conversion:

1. Identify the Radian Value: The angle given is ( \frac{7\pi}{10} ) radians.
2. Use the Conversion Factor: We multiply the radian measure by ( \frac{180^\circ}{\pi} ):
   [
   \text{Degrees} = \frac{7\pi}{10} \times \frac{180^\circ}{\pi}
   ]
3. Cancel Out (\pi): The (\pi) in the numerator and the (\pi) in the denominator cancel each other:
   [
   \text{Degrees} = \frac{7 \times 180^\circ}{10}
   ]
4. Perform the Multiplication: Now, calculate ( 7 \times 180^\circ ):
   [
   7 \times 180 = 1260
   ]
   So now we have:
   [
   \text{Degrees} = \frac{1260^\circ}{10}
   ]
5. Divide: Finally, divide (1260) by (10):
   [
   \text{Degrees} = 126^\circ
   ]

Thus, the conversion of ( \frac{7\pi}{10} ) radians to degrees results in (126^\circ).

In summary, converting radians to degrees is a straightforward process involving multiplication by ( \frac{180^\circ}{\pi} ). This conversion is essential in various applications such as geometry, physics, and engineering, where angles need to be expressed in a more intuitive form (degrees) instead of the mathematical form (radians). Understanding this conversion allows for easier interpretation of angle measures in real-world contexts.