Question

How much is 1 twelth of a turn in radians and in degrees?

Answer 1

1 twelfth of a turn is equivalent to 30 degrees or π/6 radians. A full circle is 360 degrees or 2π radians, and 1 radian is approximately 57.3 degrees.

Step-by-step explanation:

To find 1 twelfth of a turn in radians and degrees, we first need to understand the relationship between radians and degrees. A full circle, or one revolution, is equivalent to 360 degrees or 2π radians.

So, 1 twelfth of a turn in degrees is calculated as:

• 360 degrees / 12 = 30 degrees

Now, to convert this to radians, we use the fact that 1 radian is approximately 57.3 degrees. Therefore:

• 30 degrees ÷ 57.3 degrees/radian ≈ 0.5236 radians

Alternatively, since 2π radians are equal to 360 degrees, we can directly find 1 twelfth of a turn in radians by dividing 2π by 12:

• (2π / 12) radians = π/6 radians ≈ 0.5236 radians

Thus, 1 twelfth of a turn is equivalent to 30 degrees or π/6 radians.