Why else might that equation be important?

Pythagoras

Pythagoras' Theorem says that for a right angled triangle, the square of the long side equals the sum of the squares of the other two sides:

x² + y² = 1²

But 1² is just 1, so:

x² + y² = 1
(the equation of the unit circle)

Also, since x=cos and y=sin, we get:

(cos(θ))² + (sin(θ))² = 1

a useful "identity"

Important Angles: 30°, 45° and 60°

You should try to remember sin, cos and tan for the angles 30°, 45° and 60°.
Yes, yes, it is a pain to have to remember things, but it will make life easier when you know them, not just in exams, but other times when you need to do quick estimates, etc.

These are the values you should remember!