Trigonometry

Trigonometry is a branch of mathematics that deals with the relationships between the sides and the angles of triangles.
A right-angled triangle has one angle of 90 degrees. Trigonometry often focuses on right-angled triangles.
The longest side of a right-angled triangle is called the hypotenuse. The side opposite the right angle is always the hypotenuse.
The other two sides are known as the adjacent and opposite sides. The names are determined by which angle is being considered. The adjacent side is next to the chosen angle, and the opposite side is opposite the chosen angle.
There are three primary trigonometric ratios, which relate the sides of a right-angled triangle to its angles: sine (sin), cosine (cos), and tangent (tan).
The sin of an angle is defined as the ratio of the length of the opposite side to the length of the hypotenuse. This is often remembered as SOH - Sine is Opposite over Hypotenuse.
The cos of an angle is defined as the ratio of the length of the adjacent side to the length of the hypotenuse. This can be remembered as CAH - Cosine is Adjacent over Hypotenuse.
The tan of an angle is defined as the ratio of the length of the opposite side to the length of the adjacent side. This is often remembered as TOA - Tangent is Opposite over Adjacent.
The ratios can be used to calculate missing lengths or angles in a right-angled triangle.
The inverse trigonometric functions (sin⁻¹, cos⁻¹, tan⁻¹) are used to find an angle when you know the lengths of two sides.
The trigonometric formulas also apply to angles greater than 90 degrees and to negative angles. This requires knowledge of the unit circle, and is usually introduced at higher level maths.

Always remember to practice plenty of problems to become comfortable with using these trigonometric ratios. Understanding trigonometry is not just about memorising formulas, but also understanding when and how to use them.