Final answer:
To find the angles in radians passing through the origin and a given point on a circle, we use the arctangent function. For a point in the fourth quadrant, the angle is π + π/3 and its negative counterpart is -π - π/3.
Step-by-step explanation:
To find two angles in radians between -2π and 2π whose terminal sides pass through the origin and a given point on the circle in the rectangular coordinate system, we need to utilize trigonometric functions and their properties. Specifically, we utilize the arctangent or inverse tangent function to determine the angle associated with a given point's coordinates on the cartesian plane.
Considering that angles are positive when measured counter-clockwise and negative when measured clockwise, we can find that the angle for a point in the fourth quadrant can be obtained using the arctangent of the y-coordinate over the x-coordinate of the point of interest. Based on the information provided, an angle is calculated to be approximately 312°, which is approximately π + π/3 in radians, given that 180° is equivalent to π radians.
The second angle would be the negative equivalent since angles are symmetrical across the origin in a coordinate system. Therefore, if the positive angle is π + π/3, the negative angle would be -π - π/3. Thus, the two angles in radians are π + π/3 and -π - π/3.
Moving on, we must translate and interpret the given information into an application. We have derived a general strategy for summing vectors using the parallelogram rule and can measure the length and the direction angle of the resultant vector. The direction angle in the fourth quadrant can also indicate the negative measurement for these vectors.