Certainly! Let’s solve this problem step-by-step.
We know that:
[tex]\[
\sin 61^\circ = \sqrt{p}
\][/tex]
We need to find:
[tex]\[
\sin 241^\circ
\][/tex]
We can use the sine angle identity for angles greater than 180 degrees:
[tex]\[
\sin (180^\circ + \theta) = -\sin \theta
\][/tex]
Here, we notice that:
[tex]\[
241^\circ = 180^\circ + 61^\circ
\][/tex]
Therefore, applying the sine angle identity, we get:
[tex]\[
\sin 241^\circ = \sin (180^\circ + 61^\circ) = -\sin 61^\circ
\][/tex]
Given that:
[tex]\[
\sin 61^\circ = \sqrt{p}
\][/tex]
We substitute this value into our equation:
[tex]\[
\sin 241^\circ = -\sqrt{p}
\][/tex]
Therefore, the correct answer is:
[tex]\[
\sin 241^\circ = -\sqrt{p}
\][/tex]
The answer is:
[tex]\[
\boxed{-\sqrt{p}}
\][/tex]
