To determine which values are not equal to [tex]\(\sin \left(-230^{\circ}\right)\)[/tex], let's analyze the given trigonometric values step-by-step.
1. Calculate [tex]\(\sin \left(-230^\circ\right)\)[/tex]
The sine of [tex]\(-230^\circ\)[/tex] is approximately [tex]\(0.766\)[/tex].
2. Calculate [tex]\(\sin \left(-50^\circ\right)\)[/tex]
The sine of [tex]\(-50^\circ\)[/tex] is approximately [tex]\(-0.766\)[/tex].
3. Calculate [tex]\(\sin \left(130^\circ\right)\)[/tex]
The sine of [tex]\(130^\circ\)[/tex] is approximately [tex]\(0.766\)[/tex].
4. Calculate [tex]\( -\sin \left(-50^\circ\right) \)[/tex]
Since [tex]\(\sin \left(-50^\circ\right)\)[/tex] is [tex]\(-0.766\)[/tex], the negative of that value is:
[tex]\[
-(-0.766) = 0.766
\][/tex]
5. Calculate [tex]\(\sin \left(50^\circ\right)\)[/tex]
The sine of [tex]\(50^\circ\)[/tex] is approximately [tex]\(0.766\)[/tex].
Now, we compare each calculated value against [tex]\(\sin \left(-230^\circ\right)\)[/tex], which is approximately [tex]\(0.766\)[/tex].
- [tex]\(\sin \left(-50^\circ\right) \approx -0.766\)[/tex]
- [tex]\(\sin \left(130^\circ\right) \approx 0.766\)[/tex]
- [tex]\( -\sin \left(-50^\circ\right) \approx 0.766\)[/tex]
- [tex]\(\sin \left(50^\circ\right) \approx 0.766\)[/tex]
From these comparisons, we can see that [tex]\(\sin \left(-50^\circ\right)\)[/tex] which is approximately [tex]\(-0.766\)[/tex], does not equal [tex]\(\sin \left(-230^\circ\right)\)[/tex], while the others do.
Therefore, the answer is:
[tex]\[
\sin \left(-50^\circ\right)
\][/tex]
