We know that (sin 30^\circ = 1/2).

We know that (cos 60^\circ = 1/2).

We know that (tan 45^\circ = 1).

The Pythagorean identity states that in a right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides.

The sine rule states that in a triangle, the ratio of the sine of an angle to the length of the opposite side is the same for all angles.

The cosine rule states that in a triangle, the square of the length of one side is equal to the sum of the squares of the lengths of the other two sides minus twice the product of the lengths of the other two sides and the cosine of the angle between them.

The double angle formula for sine states that (sin 2A = 2 sin A cos A).

The double angle formula for cosine states that (cos 2A = cos^2 A - sin^2 A).

The double angle formula for tangent states that (tan 2A = \frac{2 tan A}{1 - tan^2 A}).

The half angle formula for sine states that (sin \frac{A}{2} = \pm \sqrt{\frac{1 - cos A}{2}}).

The half angle formula for cosine states that (cos \frac{A}{2} = \pm \sqrt{\frac{1 + cos A}{2}}).

The half angle formula for tangent states that (tan \frac{A}{2} = \pm \sqrt{\frac{1 - cos A}{1 + cos A}}).

The area of a triangle with sides (a), (b), and (c) is given by (\frac{1}{2}ab sin C), where (C) is the angle between sides (a) and (b).

The volume of a pyramid with base area (B) and height (h) is given by (\frac{1}{3}Bh).