Question
〔 5.7.2 Teet (C\$T): Trigonometry Queation 11 of 25 What is the reference angle for \( 212^{\circ} \) ? A. \( 32^{\circ} \) B. \( 42^{\circ} \) C. \( 48^{\circ} \) D. \( 58^{\circ} \)
Ask by Colon Norton. in the United States
Jan 31,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
The reference angle for \( 212^{\circ} \) is \( 32^{\circ} \).
Solution
To find the **reference angle** for \( 212^{\circ} \), follow these steps:
1. **Determine the Quadrant:**
- \( 212^{\circ} \) lies in the **third quadrant** (180° to 270°).
2. **Calculate the Reference Angle:**
- In the third quadrant, the reference angle is calculated by subtracting \( 180^{\circ} \) from the given angle.
\[
\text{Reference Angle} = 212^{\circ} - 180^{\circ} = 32^{\circ}
\]
**Answer:**
**A. \( 32^{\circ} \)**
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Simplify this solution The Deep Dive
To find the reference angle for \( 212^{\circ} \), you first determine that it lies in the third quadrant. Reference angles in this quadrant are calculated by subtracting \( 180^{\circ} \) from the angle. So, \( 212^{\circ} - 180^{\circ} = 32^{\circ} \). Hence, the reference angle is \( 32^{\circ} \)! And guess what? Reference angles are not just useful in trigonometry; they also help in understanding the behavior of periodic functions like sine and cosine. By knowing the reference angle, you can quickly figure out values for trig functions in any quadrant, saving you time on those tricky calculations!
