Formule de geometrie la matematica (sin si cos)

Formule de geometrie la matematica (sin si cos)

'2 insemna : la patrat;

'3 inseamna : la a 3-a;

(ceva) / (ceva) inseamna: supra;

-+ inseamna minus sau plus.

Pentru sinus :

1.sin (u + v) = sin u sin v + cos u cos v;

2.sin (u + v + w) = sin u cos v cos w + sin v cos w cos u +sin w cos u cos v - sin u sin v sin w;

3.sin u/2 = + radical din (1- cos u) / 2 = 1 / 2 (radical din(1+ sin u) - radical din(1 - sin u));

4.sin 2u = 2 sin u cos u = + 2 sin u radical din(1 - sin'2 u) = + 2 cos u radical din(1 - cos' 2 u);

5.sin 3u = 3 sin u cos' 2 u - sin'3 u = 3 sin u - 4 sin'3 u;

6.sin 4u = 2 sin 2u* cos 2u;

7.sin'2 u = 1 - cos 2u / 2;

8.sin'3 u = 3 sin u - sin 3u / 4;

9.sin u = (2 tg u/2) / (1 + tg'2 u/2);

10. sin u + sin v = 2 sin (u + v) / 2 cos (u -+ v) / 2;

11.sin A + sin B + sin C = 4 cos A/2 cos B/2 cos C/2;

Pentru cosinus :

1.cos (u + v) = cos u cos v -+ sin u sin v;

2.cos u cos v = [cos (u + v) + cos (u - v)]/2;

3.cos(u + v + w) = cos u cos v cos w - sin u sin v cos w - sin v sin w cos u - sin u sin w cos v;

4.cos u/2 = +radical din(1 + cos u)/2 = 1/2 (radical din(1 + sin u) + radical din(1 - sin u));

5.cos 2u = cos'2 u - sin'2 u = 2 cos'2 u - 1 = 1 - 2 sin'2 u;

6.cos 3u = cos'3 u - 3 cos u sin'2 u = 4 cos'3 u - 3 cos u;

7.cos'2 u = (1+ cos 2u) /2;

8.cos'3 u = (3 cos u + cos 3u)/4;

9.cos u = (1 - tg'2 u/2 )/(1 + tg'2 u/2 );

10.cos u + cos v = -2 sin (u + v)/2 sin (u - v)/2 = 2 sin (v + u)/2 sin (v - u)/2;

11. cos A + cos B + cos C = 1 + 4 sin A/2 sin B/2 sin C/2.

involut (in radieni)