Pregunta
Type your answer What is the reference angle of the angle \( 135^{\circ} \) ?
Ask by Sandoval Li. in the United States
Feb 03,2025
Solución de tutoría real
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The reference angle of \(135^{\circ}\) is \(45^{\circ}\).
Solución
The reference angle of \(135^{\circ}\) is \(45^{\circ}\).
**Explanation:**
A **reference angle** is the smallest acute angle that the terminal side of the given angle makes with the x-axis. To find the reference angle for \(135^{\circ}\):
1. **Determine the quadrant:**
\(135^{\circ}\) is in the **second quadrant** (between \(90^{\circ}\) and \(180^{\circ}\)).
2. **Calculate the reference angle:**
In the second quadrant, the reference angle is calculated by subtracting the given angle from \(180^{\circ}\):
\[
180^{\circ} - 135^{\circ} = 45^{\circ}
\]
So, the reference angle for \(135^{\circ}\) is **\(45^{\circ}\)**.
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Simplifique esta solución Mind Expander
The reference angle for any angle is the acute angle it makes with the x-axis. For an angle of \( 135^{\circ} \), which lies in the second quadrant, the reference angle is calculated by subtracting it from \( 180^{\circ} \). So, \( 180^{\circ} - 135^{\circ} = 45^{\circ} \). Therefore, the reference angle is \( 45^{\circ} \)! Now, here's a fun fact: reference angles are like the “introduction” to their bigger angle's story! They help us easily determine the sine, cosine, and tangent values for greater angles by giving us that familiar “acute” look. Next time you see a \( 135^{\circ} \) angle, just think of it as a cool \( 45^{\circ} \) buddy ready to party with trigonometric functions!
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