The value of $\cos 90^\circ$ is $0$.

This is because on the unit circle, at an angle of $90^\circ$ (or $\frac{\pi}{2}$ radians), the point lies at $(0, 1)$, and cosine corresponds to the x-coordinate, which is 0 at that position.

Would you like more details or have any questions?

Here are some related questions you might find interesting:

1. What is the sine of $90^\circ$?
2. How do you calculate the cosine of other common angles, like $30^\circ$ or $60^\circ$?
3. What are the trigonometric functions of angles in radians?
4. Can you explain the unit circle and its connection to trigonometry?
5. How does cosine change in different quadrants?

Tip: The cosine function is positive in the first and fourth quadrants of the unit circle and negative in the second and third.