Given an angle in standard position whose terminal side passes through the point $(1,1)$, what is the measure of angle $\mathrm{BAC}$? Round your answer to the nearest whole degree.

• A. $1°$
• B. $44°$
• C. $0°$
• D. $45°$

Answer: (D)

Verified step by step guidance

1. Identify the coordinates of the point through which the terminal side of the angle passes. Here, the point is (1, 1).
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. Substitute the coordinates into the tangent formula: \(\tan(\theta) = \frac{1}{1} = 1\).
4. Use the inverse tangent function to find the angle: \(\theta = \tan^{-1}(1)\).
5. Since \(\tan^{-1}(1)\) corresponds to an angle of 45 degrees in the first quadrant, conclude that the measure of angle \(BAC\) is approximately 45 degrees.