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

Answer 1

To find the reference angle for the angle \(\frac{3\pi}{4}\), we need to determine the angle's position in relation to the x-axis.

1. The angle \(\frac{3\pi}{4}\) is located in the second quadrant.
2. The reference angle is calculated as follows:

\[
\text{Reference Angle} = \pi - \text{Angle}
\]

So, we have:

\[
\text{Reference Angle} = \pi - \frac{3\pi}{4} = \frac{4\pi}{4} - \frac{3\pi}{4} = \frac{\pi}{4}
\]

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

The correct answer is:

\(\frac{\pi}{4}\)