If an angle $c$ in standard position has its terminal side passing through the point $(1,1)$ in the first quadrant, what is the measure of angle $c$ in degrees?

• A. $45°$
• B. $75°$
• C. $30°$
• D. $60°$

Answer: (A)

Verified step by step guidance

1. Identify the coordinates of the point through which the terminal side of angle \(c\) passes. Here, the point is \((1, 1)\), which lies in the first quadrant.
2. Recall that the tangent of an angle \(c\) in standard position is given by the ratio of the \(y\)-coordinate to the \(x\)-coordinate of the point on its terminal side: \(\tan(c) = \frac{y}{x}\).
3. Calculate \(\tan(c)\) using the given point: \(\tan(c) = \frac{1}{1} = 1\).
4. Use the inverse tangent function to find the measure of angle \(c\): \(c = \tan^{-1}(1)\).
5. Recognize that \(\tan^{-1}(1)\) corresponds to an angle of \(45^\circ\) in the first quadrant, so the measure of angle \(c\) is \(45^\circ\).