Final answer:
To find the angle θ where its terminal side passes through (7, -6√2), we look at the options and quadrant location. Since the point is in the fourth quadrant, the answer is 300°, which corresponds to option D.
Step-by-step explanation:
When asked to find the angle θ where the terminal side of θ passes through the point (7, -6√2), we need to determine the angle's measure based on the given coordinates in the Cartesian plane. The coordinates (7, -6√2) indicate that the point lies in the fourth quadrant of the Cartesian plane. In the fourth quadrant, the reference angle (the acute angle between the terminal side and the x-axis) combined with the correct quadrant position gives us the angle in a standard position. The formula for finding the angle in the unit circle with a point (x, y) is given by θ = atan2(y, x), where atan2 is the two-argument arctangent function that takes into consideration the signs of both arguments to determine the correct quadrant of the angle.
Here, we do not need to calculate the angle explicitly since we are given options. Angle θ can be found by using trigonometric ratios and understanding the properties of the unit circle. Since the point lies in the fourth quadrant and the x-coordinate is positive while the y-coordinate is negative, the terminal side of the angle is directed below the x-axis. The correct angle, θ, is 360° minus the reference angle. In this case, option D. 300° is the correct answer as it corresponds to an angle that terminates in the fourth quadrant with the given coordinates.