An angle is in standard position and its terminal side passes through the point $(3,4)$. What is the measure of the angle in degrees, rounded to the nearest whole number?

• A. $45$
• B. $60$
• C. $37$
• D. $53$

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 (3, 4).
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: \( \tan(\theta) = \frac{4}{3} \).
3. To find the angle \( \theta \), take the inverse tangent (arctangent) of \( \frac{4}{3} \): \( \theta = \tan^{-1}\left(\frac{4}{3}\right) \).
4. Calculate \( \theta \) in degrees by ensuring your calculator is set to degree mode before evaluating the inverse tangent.
5. Round the resulting angle to the nearest whole number to get the measure of the angle in degrees.