Similar triangles are triangles that have the same shape but may have different sizes. The corresponding angles of similar triangles are equal, and the corresponding sides are proportional.

SOHCAHTOA is a mnemonic used to remember the definitions of the primary trigonometric functions:

SOH stands for Sine = Opposite / Hypotenuse, CAH stands for Cosine = Adjacent / Hypotenuse, and TOA stands for Tangent = Opposite / Adjacent.

The Sine Law (also known as the Law of Sines) relates the lengths of the sides of a triangle to the sines of its angles.

The Cosine Law (also known as the Law of Cosines) relates the lengths of the sides of a triangle to the cosine of one of its angles and the lengths of the other two sides.

Special triangles refer to right triangles with angles that have specific trigonometric ratios, such as the 30-60-90 triangle and the 45-45-90 triangle. These triangles have side lengths that are in simple ratios to each other.

The unit circle is a circle with a radius of 1 unit centered at the origin of a Cartesian coordinate system. It is used to define trigonometric functions for all angles.

The CAST rule is a mnemonic used to determine the signs of the trigonometric functions in each quadrant of the unit circle: Cosine is positive in the first quadrant, Sine is positive in the second quadrant, Tangent is positive in the third quadrant, and all are positive in the fourth quadrant.

Trigonometric ratios for angles greater than 90 degrees are determined by the signs of the ratios in the corresponding acute angles.

The sine and cosine functions represent periodic oscillations and are commonly graphed as waves. The sine function oscillates between -1 and 1, while the cosine function is a shifted version of the sine function.

Radians are a unit of measurement for angles, defined as the angle subtended at the center of a circle by an arc equal in length to the radius of the circle. There are 2π2π radians in a full circle.

Trigonometric identities are equations involving trigonometric functions that are true for all values of the variables within their domains. They are used to simplify expressions and solve equations.

Solving trigonometric equations involves finding the values of the variables that satisfy the equation within a specified domain. Techniques such as factoring, substitution, and trigonometric identities are used to solve these equations.