If an angle in standard position has its terminal side passing through the point $(-3,4)$, which of the following could be the measure in degrees of the angle's reference angle $m$?

• A. $173°$
• B. $256°$
• C. $192°$
• D. $128°$

Answer: (C)

Verified step by step guidance

1. Identify the quadrant in which the terminal side of the angle lies by examining the coordinates of the point (-3, 4). Since x is negative and y is positive, the point is in the second quadrant.
2. Recall that the reference angle is the acute angle formed between the terminal side of the angle and the x-axis. In the second quadrant, the reference angle \( m \) can be found by subtracting the angle from 180°.
3. Calculate the angle \( \theta \) formed by the terminal side using the coordinates. First, find the tangent of the angle using \( \tan(\theta) = \frac{|y|}{|x|} = \frac{4}{3} \).
4. Find the angle \( \alpha \) whose tangent is \( \frac{4}{3} \) using the inverse tangent function: \( \alpha = \tan^{-1}\left(\frac{4}{3}\right) \). This angle \( \alpha \) is the reference angle \( m \) because it is the acute angle between the terminal side and the x-axis.
5. Use the reference angle \( m = \alpha \) to check which of the given options matches this value or is consistent with the quadrant and reference angle definition.