Yes, $\cos 32^\circ$ and $\sin 58^\circ$ have the same value because of the complementary angle relationship in trigonometry:

$\sin(90^\circ - \theta) = \cos(\theta)$

Here, $\theta = 32^\circ$. So,

$\sin(58^\circ) = \sin(90^\circ - 32^\circ) = \cos(32^\circ)$

Thus, $\cos 32^\circ = \sin 58^\circ$.

Do you want a detailed explanation or have any questions?

Here are five questions for you to explore further:

1. What is the complementary angle relationship in trigonometry?
2. Can this relationship be applied to angles other than acute angles?
3. What happens when we apply the relationship to obtuse angles?
4. Why are sine and cosine related through complements?
5. How would this work with radians instead of degrees?

Tip: Always remember that complementary angles ($\theta + \phi = 90^\circ$) have such symmetry in trigonometry.