Question
Find angle between 0 radians and 2pie radians that is coterminous to 11 pie over 4 radians
Answers
GPT-4o mini
To find an angle between \(0\) radians and \(2\pi\) radians that is coterminous to \(\frac{11\pi}{4}\) radians, we can subtract \(2\pi\) until the resulting angle is within the desired range.
First, we recognize that \(2\pi\) can be expressed as \(\frac{8\pi}{4}\). Now we can subtract \(2\pi\) from \(\frac{11\pi}{4}\):
\[
\frac{11\pi}{4} - \frac{8\pi}{4} = \frac{3\pi}{4}
\]
Now, \(\frac{3\pi}{4}\) is between \(0\) and \(2\pi\) (which is \(0\) to \(\frac{8\pi}{4}\)), so this is our coterminous angle.
Thus, the angle coterminous to \(\frac{11\pi}{4}\) radians that lies between \(0\) and \(2\pi\) radians is:
\[
\frac{3\pi}{4} \text{ radians}
\]
First, we recognize that \(2\pi\) can be expressed as \(\frac{8\pi}{4}\). Now we can subtract \(2\pi\) from \(\frac{11\pi}{4}\):
\[
\frac{11\pi}{4} - \frac{8\pi}{4} = \frac{3\pi}{4}
\]
Now, \(\frac{3\pi}{4}\) is between \(0\) and \(2\pi\) (which is \(0\) to \(\frac{8\pi}{4}\)), so this is our coterminous angle.
Thus, the angle coterminous to \(\frac{11\pi}{4}\) radians that lies between \(0\) and \(2\pi\) radians is:
\[
\frac{3\pi}{4} \text{ radians}
\]