Question
Find the reference angle for the angle \( 246^{\circ} \). The reference angle is \( \square \) ? (Type an integer or a decirnat)
Ask by Gonzalez Cervantes. in the United States
Dec 03,2024
Upstudy AI Solution
Tutor-Verified Answer
Answer
The reference angle is \( 66 \).
Solution
To find the reference angle for the angle \( 246^{\circ} \), we first determine which quadrant the angle is in. Since \( 246^{\circ} \) is between \( 180^{\circ} \) and \( 270^{\circ} \), it is in the third quadrant.
The reference angle \( \theta' \) for an angle in the third quadrant can be found using the formula:
\[
\theta' = \theta - 180^{\circ}
\]
Substituting \( \theta = 246^{\circ} \):
\[
\theta' = 246^{\circ} - 180^{\circ} = 66^{\circ}
\]
Thus, the reference angle for \( 246^{\circ} \) is \( 66^{\circ} \).
The reference angle is \( 66 \).
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Simplify this solution Mind Expander
To find the reference angle for \( 246^{\circ} \), you first determine which quadrant the angle is in. Since \( 246^{\circ} \) is in the third quadrant (between \( 180^{\circ} \) and \( 270^{\circ} \)), you can calculate the reference angle by subtracting \( 246^{\circ} \) from \( 360^{\circ} \), or alternatively, subtracting it from \( 180^{\circ} \) and then taking the absolute value of the result—both methods will give you the same reference angle in the third quadrant. Thus, the reference angle is: \[ \text{Reference Angle} = 246^{\circ} - 180^{\circ} = 66^{\circ}. \] So, the reference angle is \( 66^{\circ} \).
