Реферат: Тригонометрия алгебра
(a-b)3=a3-3a2b+3ab2-b3
a3+b3=(a+b)(a2-ab+b2)
a3-b3=(a-b)(a2+ab+ b2)
| 0 | p/6 | p/4 | p/3 | p/2 | p | 2/3p | 3/4p | 5/6p | 3/2p | |
|
| 0 | 30° | 45° | 60° | 90° | 180 | 120° | 135° | 150° | 270° |
| sin | 0 | 1/2 | Ц2/2 | Ц3/2 | 1 | 0 | Ц3/2 | Ц2/2 | 1/2 | -1 |
| cos | 1 | Ц3/2 | Ц2/2 | 1/2 | 0 | -1 | -1/2 | -Ц2/2 | -Ц3/2 | 0 |
| tg | 0 | 1/Ц3 | 1 | Ц3 | - | 0 | -Ц3 | -1 | -1/Ц3 | - |
| ctg | - | Ц3 | 1 | 1/Ц3 | 0 | - | -1/Ц3 | -1 | -Ц3 | 0 |
sin2+cos2=1 sin=±Ц1-cos2 sin(-a)=-sina tg(-a)=-tga
tg•ctg=1 cos=±Ц1-sin2 cos(-a)=cosa ctg(-g)=-ctga
tg=1/ctg ctg=1/tg 1+tg2=1/cos2=sec2
sin2=(1-cos)(1+cos) 1+ctg2=1/sin2=cosec2 sin2a=2sina•cosa
cos2=(1-sin)(1+sin) 1-tg2/(1+tg2)=cos4-sin4 cos2a=cos2 a-sin2 a
cos/(1-sin)=1+sin/cos 1/(tg+ctg)=sin•cos tg2a=2tga/1-tga
cos(a+b)=cosa•cosb-sina•sinb sin3a=3sina-4sin3a
cos(a-b)=cosa•cosb+sina•sinb cos3a=4cos3a-3cosa
sin(a+b)=sina•cosb+cosa•sinb tg(a+b)=tga+tgb
sin(a-b)=sina•cosb-cosa•sinb 1-tga•tgb
2cos2a/2=1+cosa 2sin2a/2=1-cosa
| 0 | p/6 | p/4 | p/3 | p/2 | p | 2/3p | 3/4p | 5/6p | 3/2p | |
| 0 | 30° | 45° | 60° | 90° | 180 | 120° | 135° | 150° | 270° | |
| sin | 0 | 1/2 | Ц2/2 | Ц3/2 | 1 | 0 | Ц3/2 | Ц2/2 | 1/2 | -1 |
|
| 1 | Ц3/2 | Ц2/2 | 1/2 | 0 | -1 | -1/2 | -Ц2/2 | -Ц3/2 | 0 |
| tg | 0 | 1/Ц3 | 1 | Ц3 | - | 0 | -Ц3 | -1 | -1/Ц3 | - |
| ctg | - | Ц3 | 1 | 1/Ц3 | 0 | - | -1/Ц3 | -1 | -Ц3 | 0 |
cossin2+cos2=1 sin=±Ц1-cos2 sin(-a)=-sina tg(-a)=-tga
tg•ctg=1 cos=±Ц1-sin2 cos(-a)=cosa ctg(-g)=-ctga
tg=1/ctg ctg=1/tg 1+tg2=1/cos2=sec2
sin2=(1-cos)(1+cos) 1+ctg2=1/sin2=cosec2 sin2a=2sina•cosa
cos2=(1-sin)(1+sin) 1-tg2/(1+tg2)=cos4-sin4 cos2a=cos2 a-sin2 a
cos/(1-sin)=1+sin/cos 1/(tg+ctg)=sin•cos tg2a=2tga/1-tga
cos(a+b)=cosa•cosb-sina•sinb sin3a=3sina-4sin3a
cos(a-b)=cosa•cosb+sina•sinb cos3a=4cos3a-3cosa
sin(a+b)=sina•cosb+cosa•sinb tg(a+b)=tga+tgb
sin(a-b)=sina•cosb-cosa•sinb 1-tga•tgb
sin(2p-a)=-sina sin(3p/2-a)=-cosa
cos(2p-a)=cosa cos(3p/2-a)=-sina
tg(2p-a)=-tga tg(3p/2-a)=ctga