Final answer:
The sine of π/7 is not a value that can be expressed in a simple radical form; it must be approximated using a calculator and will be between 0 and 1. One must ensure that the calculator is set to radian mode before calculating.
Step-by-step explanation:
To find the value of sin (π/7), we must understand that this is not one of the common angles for which we can find an exact trigonometric value easily. For such angles, trigonometric values can often be found using special triangles or the unit circle. However, since π/7 (approximately 0.4488 radians) does not correspond to a well-known angle, we cannot easily express its sine value in a simple radical form. Therefore, to find the value of sin (π/7), we would typically use a calculator.
Upon using a calculator, the value of sin (π/7) can be determined to a high degree of precision. While a step-by-step explanation is not applicable in this case, you should ensure that your calculator is set to radian mode since the angle is given in radians. After calculating, we will round the result to five decimal places to meet the question's requirements.
To check if the answer is reasonable, remember that the sine function varies between -1 and 1, so any result you get should fall within this range. Additionally, since π/7 is a positive angle less than π/2, we expect the sine value to also be positive and less than 1.