If an angle in standard position has its terminal side passing through the point $P(3,3)$, what is the measure of the angle in degrees?

• A. $45°$
• B. $54°$
• C. $24°$
• D. $9°$

Answer: (A)

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 P(3, 3).
2. Recall that the angle \( \theta \) in standard position can be found using the tangent function, where \( \tan(\theta) = \frac{y}{x} \). Substitute the coordinates: \( \tan(\theta) = \frac{3}{3} \).
3. Simplify the fraction to get \( \tan(\theta) = 1 \).
4. Use the inverse tangent function to find the angle: \( \theta = \tan^{-1}(1) \).
5. Convert the angle from radians to degrees if necessary, and identify the angle measure from the given options.