Final answer:
By converting 10π/3 to an equivalent angle between 0 and 2π, and then finding the acute angle it forms with the x-axis, we determine that the reference angle is π/3, making the correct answer option A) π/3.
Step-by-step explanation:
The question is about finding the reference angle for the angle 10π/3. To find a reference angle for any angle in standard position, we first need to determine the equivalent angle between 0 and 2π (0 and 360 degrees). Since the circle has 2π radians, we can subtract 2π until we get an angle in the desired range.
Starting with 10π/3, we subtract 2π, which is the same as subtracting 6π/3 to keep a common denominator:
10π/3 - 6π/3 = 4π/3
We note that 4π/3 still lies in the second or third quadrants for angles since it's greater than π (180 degrees) and less than 2π (360 degrees) where we're looking for a reference angle within the first quadrant. So, we subtract π (3π/3), the equivalent of 180 degrees to find it:
4π/3 - 3π/3 = π/3
Thus, the reference angle for 10π/3 is π/3 which makes the correct option (A) π/3.