If an angle $\mathrm{AOC}$ is in standard position and its terminal side passes through the point $(1,1)$ on the coordinate plane, what is the measure of angle $\mathrm{AOC}$ to the nearest degree?

• A. $45°$
• B. $79°$
• C. $66°$
• D. $58°$

Answer: (A)

Verified step by step guidance

1. Identify that the angle \( AOC \) is in standard position, meaning its vertex is at the origin \( O(0,0) \) and its initial side lies along the positive x-axis.
2. Note that the terminal side of the angle passes through the point \( (1,1) \). This point gives the coordinates \( x = 1 \) and \( y = 1 \).
3. Recall that the measure of the angle \( \theta \) in standard position can be found using the tangent function: \( \tan(\theta) = \frac{y}{x} \). Substitute the values to get \( \tan(\theta) = \frac{1}{1} = 1 \).
4. Use the inverse tangent function to find the angle: \( \theta = \tan^{-1}(1) \). This will give the angle in radians or degrees depending on your calculator settings.
5. Convert the angle to degrees if necessary and round to the nearest degree to find the measure of angle \( AOC \).