Final answer:
To find the principal angle of a point in standard position, you can use the inverse tangent function. In this case, the x-coordinate is -6 and the y-coordinate is 7. So, the principal angle can be found as arctan(7/-6), which is approximately -52.2 degrees. However, we need to convert this angle to the standard position by adding 360 degrees, since the point is in the second quadrant. Adding 360 to -52.2 gives us approximately 307.8 degrees. Rounding this to the nearest degree, the value of the principal angle is 308 degrees.
Step-by-step explanation:
To find the principal angle of a point in standard position, we can use the inverse tangent function. In this case, the x-coordinate is -6 and the y-coordinate is 7. So, the principal angle can be found as arctan(7/-6). Evaluating this using a calculator, we get approximately -52.2 degrees. However, we need to convert this angle to the standard position by adding 360 degrees, since the point is in the second quadrant. Adding 360 to -52.2 gives us approximately 307.8 degrees. Rounding this to the nearest degree, the value of the principal angle is 308 degrees. Therefore, the correct answer is (D) 308°.