If an angle is in standard position and its terminal side passes through the point $(1,1)$, what is the measure of the angle in degrees?

• A. $45°$
• B. $46°$
• C. $91°$
• D. $146°$

Answer: (A)

Verified step by step guidance

1. Identify that the angle is in standard position, meaning its vertex is at the origin (0,0) and its initial side lies along the positive x-axis.
2. Recognize that the terminal side of the angle passes through the point (1, 1), which lies in the first quadrant where both x and y are positive.
3. Use the coordinates of the point to find the tangent of the angle, since \( \tan(\theta) = \frac{y}{x} \). Here, \( \tan(\theta) = \frac{1}{1} = 1 \).
4. Find the angle \( \theta \) whose tangent is 1 by using the inverse tangent function: \( \theta = \tan^{-1}(1) \).
5. Convert the angle from radians to degrees if necessary, and identify which of the given options corresponds to this angle in degrees.