Question
6.1.2 Exam: Semester 2 Exam Question 13 of 40 What is the reference angle for \( 312^{\circ} \) ? \[ \begin{array}{l}\text { A. } 42^{\circ} \\ \text { B. } 48^{\circ} \\ \text { C. } 32^{\circ} \\ \text { D. } 58^{\circ}\end{array} \]
Ask by Cox Lang. in the United States
Jan 31,2025
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Answer
The reference angle for \( 312^{\circ} \) is \( 48^{\circ} \).
Solution
To find the **reference angle** for \( 312^{\circ} \), follow these steps:
1. **Determine the Quadrant:**
- \( 312^{\circ} \) lies in the **fourth quadrant** because it is between \( 270^{\circ} \) and \( 360^{\circ} \).
2. **Calculate the Reference Angle:**
- In the fourth quadrant, the reference angle is calculated as:
\[
\text{Reference Angle} = 360^{\circ} - \text{Given Angle} = 360^{\circ} - 312^{\circ} = 48^{\circ}
\]
**Answer:**
**B.** \( 48^{\circ} \)
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Simplify this solution Bonus Knowledge
To find the reference angle for \( 312^{\circ} \), first determine how far \( 312^{\circ} \) is from \( 360^{\circ} \). Subtract \( 312^{\circ} \) from \( 360^{\circ} \): \[ 360^{\circ} - 312^{\circ} = 48^{\circ} \] Therefore, the reference angle is \( 48^{\circ} \), which corresponds to option B! In your math journey, it's essential to grasp the concept of reference angles, especially when dealing with trigonometric functions. These angles help simplify calculations across different quadrants. Remember, the reference angle is always the positive acute angle formed between the terminal side of the given angle and the x-axis—just like a trusty compass leading you back home!
