Final answer:
The reference angle for 4π/3 radians is found by subtracting it from 2π, resulting in a reference angle of 2.0944 radians when rounded to four decimal places.
Step-by-step explanation:
To find the reference angle 'θ' for an angle of 4π/3 radians, we need to consider the angle's location on the unit circle. The angle 4π/3 radians is located in the third quadrant, where both x and y coordinates are negative.
The reference angle is the acute angle that the terminal side of your given angle makes with the x-axis. Since 4π/3 radians is more than π but less than 3π/2, we subtract it from 2π to find the reference angle for angles in the third quadrant:
Reference Angle = 2π - 4π/3
Now, perform the subtraction:
= 6π/3 - 4π/3
= 2π/3 radians
The reference angle in decimal form (rounded to four decimal places as per the question) is:
= 2.0944 radians (since π ≈ 3.1416)