Which angle measure is closest to 8 radians?
A. 100 degs
B. 120 degs
C. 150 degs
D. 360 degs
8 * 180/pi = 458.4
Even without knowing that, you know that 8 > 2pi, so 360 is the closest of the choices.
To convert radians to degrees, we can use the formula:
Degrees = Radians * (180 / π)
Let's calculate the angle measure in degrees:
Degrees = 8 * (180 / π)
Degrees ≈ 458.366 degrees
Among the given options, the angle measure that is closest to 8 radians is:
D. 360 degrees
To determine which angle measure is closest to 8 radians, we need to convert the given options from degrees to radians and compare them to 8 radians.
The conversion from degrees to radians is given by the formula:
radians = degrees * (pi / 180)
Using this formula, we can convert each option:
A. 100 degrees = 100 * (pi / 180) radians ≈ 1.745 radians
B. 120 degrees = 120 * (pi / 180) radians ≈ 2.094 radians
C. 150 degrees = 150 * (pi / 180) radians ≈ 2.618 radians
D. 360 degrees = 360 * (pi / 180) radians ≈ 6.283 radians
Now that we have the conversions, we can compare these values with 8 radians:
A. 1.745 radians is less than 8 radians.
B. 2.094 radians is less than 8 radians.
C. 2.618 radians is less than 8 radians.
D. 6.283 radians is greater than 8 radians.
From the comparisons, we can see that the option closest to 8 radians is D. 360 degrees.
So the correct answer is D. 360 degs.