Trigonometry is the branch of mathematics that studies triangles and their parts - angles and sides. Trigonometry is the study of triangles, their angles, and their sides. It is especially about right triangles, but you extend it to apply to all triangles.
When you know three of a triangle's six parts (three sides and three angles), you can get all six parts, provided one of the given parts is the length of a side. This is called solving the triangle.
Six trigonometric functions describe the relationships between the sides of a triangle. Three are very important, and the other three are reciprocal functions, defined as the reciprocals of the main functions.
Angle A faces the side called the opposite side. It’s next to the side called the adjacent side. The remaining side is the hypotenuse, which is always the longest side in a right triangle.
1. The sine (abbreviated sin) is the ratio of the opposite side to the hypotenuse.
sin A = a/c
2. The cosine (abbreviated cos) is the ratio of the adjacent side to the hypotenuse.
cos A = b/c
3. The tangent (abbreviated tan) is the ratio of the opposite side to the adjacent side.
tan A = a/b
4. The cosecant (abbreviated csc) is a variation of the sine function. It’s the ratio of the hypotenuse to the opposite side.
csc A = c/a
5. The secant (abbreviated sec) is a variation of the cosine function. It’s the ratio of the hypotenuse to the adjacent side.
sec A = c/b
6. The cotangent (abbreviated cot) is a variation of the tangent function, but with the terms inverted. It’s the ratio of the adjacent side to the opposite side.
cot A = b/a
The law of sines states that
a/Sin A = b/Sin B = c/Sin C
This law applies to any triangle with sides a, b, and c and angles A, B, and C, where A is the angle opposite side a, B is the angle opposite side b, and C is the angle opposite side c.
The value of the law of sines is that when you know three measurements of a triangle (as long as they include at least one side), you solve for the fourth measurement with no problem. You must have two angles and a side or two sides and an angle.