Question
Find the reference angle for the angle \( 127^{\circ} \) The reference angle is \( \square^{\circ} \) (ivpe an integer or a decimin.)
Ask by Delgado Harrington. in the United States
Dec 03,2024
Upstudy AI Solution
Tutor-Verified Answer
Answer
The reference angle is \( 53^{\circ} \).
Solution
To find the reference angle for an angle of \( 127^{\circ} \), we first determine which quadrant the angle is in. Since \( 127^{\circ} \) is between \( 90^{\circ} \) and \( 180^{\circ} \), it is in the second quadrant.
The reference angle \( \theta' \) for an angle in the second quadrant can be found using the formula:
\[
\theta' = 180^{\circ} - \theta
\]
where \( \theta \) is the given angle.
Substituting \( \theta = 127^{\circ} \):
\[
\theta' = 180^{\circ} - 127^{\circ} = 53^{\circ}
\]
Thus, the reference angle for \( 127^{\circ} \) is \( 53^{\circ} \).
The reference angle is \( \boxed{53} \).
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Simplify this solution Mind Expander
To find the reference angle for \( 127^{\circ} \), you'll want to subtract it from \( 180^{\circ} \) since it lies in the second quadrant. So, \( 180^{\circ} - 127^{\circ} = 53^{\circ} \). Therefore, the reference angle is \( 53^{\circ} \). Now that you know how to find reference angles, remember that they are always positive and less than \( 90^{\circ} \). They are particularly useful in trigonometry to simplify calculations for the sine, cosine, and tangent of angles in different quadrants. It's like giving a tricky angle a makeover to make it more manageable!
