If \( \sin 34^{\circ}=p \), determine the following interms of \( p \). \( \cos \left(-56^{\circ}\right) \)

To find \( \cos(-56^{\circ}) \), we can use the cosine identity that states that \( \cos(-\theta) = \cos(\theta) \). Therefore, \[ \cos(-56^{\circ}) = \cos(56^{\circ}). \] Now, we can relate \( \cos(56^{\circ}) \) to \( \sin(34^{\circ}) \) using the complementary angle identity, which is \[ \cos(90^{\circ} - \theta) = \sin(\theta). \] Applying this, we have: \[ \cos(56^{\circ}) = \cos(90^{\circ} - 34^{\circ}) = \sin(34^{\circ}). \] Since \( \sin(34^{\circ} = p\), we can conclude that \[ \cos(-56^{\circ}) = p. \] Thus, the final answer is \[ \cos(-56^{\circ}) = p. \]