If angle $\mathrm{COA}$ is in standard position and its terminal side passes through the point (−$1$, $2$), what is the measure of angle $\mathrm{COA}$ to the nearest degree?

• A. $150°$
• B. $170°$
• C. $116°$
• D. $140°$

Answer: (C)

Verified step by step guidance

1. Identify the coordinates of the point through which the terminal side of angle COA passes. Here, the point is (-1, 2).
2. Recall that the angle in standard position is measured from the positive x-axis to the terminal side. To find this angle, we can use the tangent function, which relates the y-coordinate and x-coordinate of the point: \(\tan(\theta) = \frac{y}{x}\).
3. Calculate the reference angle \(\theta_r\) by taking the arctangent of the absolute values of the coordinates: \(\theta_r = \arctan\left(\left|\frac{2}{-1}\right|\right) = \arctan(2)\).
4. Determine the quadrant where the point (-1, 2) lies. Since x is negative and y is positive, the point is in the second quadrant. Angles in the second quadrant are calculated as \(\theta = 180^\circ - \theta_r\).
5. Substitute the reference angle into the formula to find the measure of angle COA: \(\theta = 180^\circ - \arctan(2)\). This will give the angle in degrees, which you can then round to the nearest degree.