Questions: (x, y)=(2,6)

Solution Steps

To solve this problem, we need to determine the angle between the vector (x, y) and the positive x-axis. This can be done using the arctangent function (atan2) which gives the angle in radians. We then convert the angle from radians to degrees.

Given the coordinates \((x, y) = (2, 6)\), we use the arctangent function to find the angle in radians: \[ \theta_{\text{radians}} = \arctan\left(\frac{y}{x}\right) = \arctan\left(\frac{6}{2}\right) = 1.2490 \text{ radians} \]

To convert the angle from radians to degrees, we use the conversion factor \(\frac{180}{\pi}\): \[ \theta_{\text{degrees}} = \theta_{\text{radians}} \times \frac{180}{\pi} = 1.2490 \times \frac{180}{\pi} = 71.5651^\circ \]

Final Answer