Final answer:
The positive co-terminal angle with an angle that measures (4π)/3 radians is found by adding 2π to (4π)/3, resulting in 10π/3 radians. Converting this to degrees gives us 600 degrees.
Step-by-step explanation:
The student asked: What is the positive angle that is co-terminal with an angle that measures (4π)/3? Firstly, we must understand that the angle mentioned is in radians and we are looking for its co-terminal angle, meaning an angle that differs from the given angle by an integer multiple of 2π. One full rotation in a circle is 360 degrees, which is equivalent to 2π radians. So to find a co-terminal angle, we can add or subtract multiples of 2π.
The angle of (4π)/3 is more than π but less than 2π, which means it is between 180 to 360 degrees in degree measure. To get a positive co-terminal angle, we can simply add 2π to (4π)/3:
(4π)/3 + 2π = (4π + 6π)/3 = 10π/3 radians
Now, 10π/3 is the positive co-terminal angle of (4π)/3 radians. If we want this in degrees, we can use the conversion that 180 degrees = π radians, resulting in:
10π/3 radians * (180 degrees/π radians) = 600 degrees
Therefore, the positive co-terminal angle with an angle that measures (4π)/3 radians is 600 degrees.