Formule trigonometrie

sin2x+cos2x=1

Reducerea la primul cadran

sin(x+2kπ)=sinx

cos(x+2kπ)=cosx

tg(x+kπ)=tgx

ctg(x+kπ)=ctgx

sin(x + π2 )=cosx

cos(π2 - x)=sinx cos(3π2 - x)=-sinx

tg(π2 - x)=ctgx

ctg(π2 - x)=tgx

sin(kπ+x)=sinxcos(kπ+x)=cosx

tg(kπ+/-x)=tgxctg(kπ+/-x)=ctgx

In general:

sin[ (2k+1)π2+ x ]=cosx

cos[ (2k+1)π2+ x ]=sinx

tg[ (2k+1)π2+¿−¿¿¿

¿

x ]=ctgx

ctg[ (2k+1)π2 +¿−¿¿¿¿

x ]=tgx

CU SEMNUL DIN CADRAN!!!

sin(a+¿−¿¿¿¿ b)=sina*cosb+¿−¿¿¿

¿ sinb*cosacos(a+b)=cosa*cosb-sina*sinb

cos(a-b)=cosa*cosb+sina*sinb

tg(a+b)= tga+tgb1−tga∗tgb

tg(a-b)= tga−tgb1+ tga∗tgb

sina+sinb= 2sina+b2 *cosa−b2

sina-sinb= 2sina−b2 *cosa+b2

cosa+cosb=2cosa+b2 *cosa−b2

cosa-cosb=-2sina+b2 *sina−b2

sina*cosb=12[sin(a+b) + sin(a-b)]

cosa*cosb= 12[cos(a+b) + cos(a-b)]

sina*sinb=12[cos(a-b) - cos(a+b)]

PARANTEZE!!!

SUMA IN PRODUS!!!

PRODUS IN SUMA!!!

sin2a= 2sina*cosa

cos2a=cos2a-sin2a

1-2sin2a 2a

2*cos2a−1

tg2a= 2 tga

1−tg2a

t=tga2 = sina1+cosa=

1−cosasina

sina= 2t

1+ t2

cosa=1−t2

1+t2 IN FUNCTIE DE TG

tga== 2 t

1−t 2

sina2= +¿−¿¿¿¿ √ 1−cosa2

SIN,COSa2

cosa2= +¿−¿¿¿¿ √ 1+cosa2

x0˚ 30˚ 45˚ 60˚ 90˚ 180˚ 270˚ 360˚

π6

π4

π3

π2

π 3π2

2 π

Sinx0

12

√22

√32

1 0 -1 0

Cosx 1 √32

√22

12

0 -1 0 1

Tgx 0 √33

1 √3 - 0 - 0

Ctgx - √3 1 √33

0 - 0 -