Question

Find the reference angle for the angle Start Fraction 3 pi over 4 End Fraction.
(1 point)
Responses

Start Fraction 4 pi over 3 End Fraction
Image with alt text: Start Fraction 4 pi over 3 End Fraction

Start Fraction pi over 4 End Fraction
Image with alt text: Start Fraction pi over 4 End Fraction

Start Fraction pi over 3 End Fraction
Image with alt text: Start Fraction pi over 3 End Fraction

Start Fraction pi over 6 End Fraction
Image with alt text: Start Fraction pi over 6 End Fraction

Answer 1

To find the reference angle for the angle \( \frac{3\pi}{4} \), you first need to determine which quadrant the angle is in.

The angle \( \frac{3\pi}{4} \) is in the second quadrant because:
- \( \pi \) (or \( \frac{4\pi}{4} \)) is the straight angle, and
- \( \frac{3\pi}{4} \) is greater than \( \frac{\pi}{2} \) (or \( \frac{2\pi}{4} \)) but less than \( \pi \).

The reference angle is calculated using the formula:
- Reference Angle = \( \pi - \theta \) (for angles in the second quadrant).

So, for \( \theta = \frac{3\pi}{4} \):
\[
\text{Reference Angle} = \pi - \frac{3\pi}{4} = \frac{4\pi}{4} - \frac{3\pi}{4} = \frac{\pi}{4}.
\]

Thus, the reference angle for \( \frac{3\pi}{4} \) is \( \frac{\pi}{4} \).

The correct response is:
**Start Fraction pi over 4 End Fraction**