TRIGONOMETRY: Sine law, Law of cosines, pythagorean identities, trigonometric identities, double angle formulas, reduction formulas, power-reducing formulas, common right triangle combination sides

Below are the most important and most useful formulas in Trigonometry which have so many applications in various fields of study, discipline and professions:

1. Sine Law (Law of Sines)
2. Cosine Law (Law of Cosines)
3. Pythagorean Theorem
4. Pythagorean Identities, Twice angle formulas
5. Double angle formulas
6. Power - reducing theorem
7. Radian measure, Reduction formulas

let:

t, theta = angle measure

a = shortest side of triangle

b = medium side of triangle

c = longest side of triangle

A = angle opposite a

B = angle opposite b

C = angle opposite c



Right Triangles

45 x 45:

a = b = 1

c = sqrt 2 = 1.4


30 x 60:

a = 1

b = sqrt 3 = 1.7

c = 2


Common Right Triangle combinations

3,4,5 ---> a=3, b=4, c=5

5,12,13 ---> a=5, b=12, c=13
 

Sine Law (Law of Sines):