3/5 of a revolution represents approximately how many radians?
Question 12 options:
6.28
3.14
3.77
108.00
3.77
One rotation is 2π radians
so (3/5)(2π) = ......
Well, if we're talking about a revolution, that's a full circle. And a full circle is equal to 2π radians. So if 2π is a full circle, then 3/5 of a revolution would be approximately 3/5 times 2π. That gets us to about 3.77 radians. So, the answer is C: 3.77 radians.
To find the number of radians that 3/5 of a revolution represents, we need to first determine the number of radians in a full revolution.
One revolution is equivalent to 360 degrees. Since there are 2π radians in a full circle (or 360 degrees), we can convert this into radians by multiplying by π/180:
1 revolution = 360 degrees = 360 * (π/180) radians
= 2π radians
Now we can find the number of radians that 3/5 of a revolution represents:
(3/5) * 2π radians
= (3 * 2π)/5 radians
= 6π/5 radians
So, 3/5 of a revolution represents approximately 6π/5 radians.
Now, let's convert this to a decimal approximation:
6π/5 ≈ 1.885 radians
Therefore, approximately 3/5 of a revolution represents 1.885 radians.
None of the given options (6.28, 3.14, 3.77, 108.00) match this answer.
To find the number of radians that 3/5 of a revolution represents, we need to know that a full revolution is equal to 2π radians.
1 revolution = 2π radians
To find the number of radians for 3/5 of a revolution, we can set up a proportion:
(3/5) revolution = x radians
1 revolution = 2π radians
Using cross-multiplication, we can find x:
(3/5) revolution * (2π radians/1 revolution) = x radians
Simplifying,
(3/5) * (2π) = x radians
Multiplying,
(3/5) * (2π) = 6π/5
So, 3/5 of a revolution represents approximately 6π/5 radians.
To evaluate this as a decimal, we know that π is approximately 3.14. Substituting this value,
6π/5 = (6 * 3.14) / 5 = 18.84/5 ≈ 3.77.
Therefore, 3/5 of a revolution represents approximately 3.77 radians.
The answer is 3.77 (option C).