Question
Sketch the angle then find its reference angle
-515^•
-515^•
Answers
GPT-4o mini
To find the reference angle for \(-515^\circ\), we first need to convert this angle into a standard position angle, which is between \(0^\circ\) and \(360^\circ\).
1. **Add \(360^\circ\) until the angle is positive:**
\[
-515^\circ + 360^\circ = -155^\circ
\]
\[
-155^\circ + 360^\circ = 205^\circ
\]
Now, we have \(205^\circ\) in standard position.
2. **Find the reference angle:**
The reference angle is the acute angle that the terminal side of the given angle makes with the x-axis. Since \(205^\circ\) lies in the third quadrant, we can find the reference angle using the following formula:
\[
\text{Reference angle} = \theta - 180^\circ
\]
\[
\text{Reference angle} = 205^\circ - 180^\circ = 25^\circ
\]
So, the reference angle for \(-515^\circ\) is \(\boxed{25^\circ}\).
1. **Add \(360^\circ\) until the angle is positive:**
\[
-515^\circ + 360^\circ = -155^\circ
\]
\[
-155^\circ + 360^\circ = 205^\circ
\]
Now, we have \(205^\circ\) in standard position.
2. **Find the reference angle:**
The reference angle is the acute angle that the terminal side of the given angle makes with the x-axis. Since \(205^\circ\) lies in the third quadrant, we can find the reference angle using the following formula:
\[
\text{Reference angle} = \theta - 180^\circ
\]
\[
\text{Reference angle} = 205^\circ - 180^\circ = 25^\circ
\]
So, the reference angle for \(-515^\circ\) is \(\boxed{25^\circ}\).