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

To find \( \cos(-56^{\circ}) \) in terms of \( p \), we can use the cosine identity and the relationship between sine and cosine. 1. **Use the cosine identity**: \[ \cos(-\theta) = \cos(\theta) \] Therefore, \[ \cos(-56^{\circ}) = \cos(56^{\circ}) \] 2. **Use the complementary angle identity**: We know that: \[ \cos(90^{\circ} - \theta) = \sin(\theta) \] Thus, \[ \cos(56^{\circ}) = \sin(90^{\circ} - 56^{\circ}) = \sin(34^{\circ} \] 3. **Substituting the known value**: Since \( \sin(34^{\circ}) = p \), we can substitute: \[ \cos(56^{\circ}) = p \] Putting it all together, we find: \[ \cos(-56^{\circ}) = p \] Thus, the final answer is: \[ \cos(-56^{\circ}) = p \]