If $\theta$ is an angle in standard position such that $\theta >180°$ and $\theta <360°$, which equation can be used to determine the reference angle $r$?

• A. $r=\theta$
• B. $r=180°-\theta$
• C. $r=360°-\theta$
• D. $r=\theta -180°$

Answer: (C)

Verified step by step guidance

1. Identify the quadrant in which the angle \( \theta \) lies. Since \( 180^\circ < \theta < 360^\circ \), \( \theta \) is in either the third or fourth quadrant.
2. Recall that the reference angle \( r \) is the acute angle formed between the terminal side of \( \theta \) and the x-axis.
3. For angles in the third quadrant (between \( 180^\circ \) and \( 270^\circ \)), the reference angle is calculated as \( r = \theta - 180^\circ \).
4. For angles in the fourth quadrant (between \( 270^\circ \) and \( 360^\circ \)), the reference angle is calculated as \( r = 360^\circ - \theta \).
5. Since the problem states \( 180^\circ < \theta < 360^\circ \) without specifying the quadrant, the general formula to find the reference angle \( r \) when \( \theta \) is in the fourth quadrant is \( r = 360^\circ - \theta \).