If an angle in standard position has its terminal side passing through the point $(-3,4)$, what is the measure of the angle in degrees?

• A. $228°$
• B. $246°$
• C. $123°$
• D. $114°$

Answer: (C)

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. Calculate the reference angle \(\theta_r\) by finding the angle the terminal side makes with the x-axis using the tangent function: \(\tan \theta_r = \left|\frac{y}{x}\right| = \left|\frac{4}{-3}\right| = \frac{4}{3}\).
3. Find the reference angle \(\theta_r\) by taking the arctangent (inverse tangent) of \(\frac{4}{3}\): \(\theta_r = \arctan\left(\frac{4}{3}\right)\).
4. Determine the quadrant in which the point \((-3, 4)\) lies. Since \(x\) is negative and \(y\) is positive, the point is in the second quadrant.
5. Calculate the actual angle \(\theta\) in standard position by subtracting the reference angle from \$180^\circ\( because angles in the second quadrant are \)180^\circ - \theta_r\(: \)\theta = 180^\circ - \theta_r$.