sin α | cos α | tg α | ctg α | |
0< α <π/2 | + | + | + | + |
π/2< α < π | + | |||
π< α <3π/2 | + | + | ||
3π/2< α <2π | + |
π/6 | π/4 | π/3 | π/2 | π | 3π/2 | 2π | ||
00 | 300 | 450 | 600 | 900 | 1800 | 2700 | 3600 | |
sin α | ½ | √2/2 | √3/2 | 1 | ||||
cos α | √3/2 | √2/2 | ½ | 1 | ||||
tg α | √3/3 | √3 | ∞ | ∞ | ||||
ctg α | ∞ | √3 | √3/3 | ∞ | ∞ |
. .
sin | cos | tg | ctg | ||
α | sinα | cosα | tgα | ctgα | |
π/2 α | cosα | sinα | ctgα | tgα | |
π α | sinα | cosα | tgα | ctgα |
sin2α + cos2α = 1; tgα ctgα = 1; tgα = sinα/cosα = 1/ctgα;
ctgα = cosα/sinα = 1/tgα; 1 + tg2α = 1/cos2α; 1 + ctg2α = 1/sin2α; secα = 1/cosα; cosecα = 1/sinα;
sinα cosα 2π, tgα ctgα π.
sin(α + 2πn) = sinα, n Z; cos(α + 2πn) = cosα, n Z; tg(α + πn) = tgα, n Z; ctg(α + πn) = ctgα, n Z;
.
sin(α β) = sinα cosβ cosα sinβ; cos(α β) = cosα cosβ sinα sinβ;
tg(α β) = (tgα tgβ) / (1 tgα tgβ); ctg(α β) = (ctgα ctgβ 1) / (ctgβ ctgα);
sin2α = 2sinα cosα; cos2α = cos2α sin2α = 12sin2α = 2cos2α 1;
tg2α = 2tgα / (1tg2α); ctg2α = (ctg2α 1) / 2ctgα;
sin(α/2) = cos(α/2) = tg(α/2) =
2sin2(α/2) = 1 cosα; 2cos2(α/2) = 1 + cosα; sin2α = (1cos2α) / 2
sinα = 2tg(α/2) / (1+ tg2(α/2)); cosα = (1tg2(α/2)) / (1+tg2(α/2)); tgα = 2tg(α/2) / (1tg2(α/2));
sin3α = 3sinα 4sin3α; cos3α = 4cos3α 3cosα;
sinα cosβ = ½ (sin(α + β) + sin(α β)); cosα cosβ = ½ (cos(α + β) + cos(α β));
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sinα sinβ = ½ cos(α β) cos(α + β));
sinα + sinβ = 2 sin((α + β)/2) cos((α β)/2); sinα sinβ = 2 sin((α β)/2) cos((α + β)/2);
cosα + cosβ = 2 cos((α + β)/2) cos((α β)/2); cosα cosβ = 2 sin((α + β)/2) sin((α β)/2);
tgα tgβ = sin(α β) / (cosα cosβ); cosα sinα = ;
sinα = a, α = arcsin a + 2πn, n Z;
α = π arcsin a + 2πn, n Z;
cosα = a, α = arccos a + 2π n, n Z;
tgα = a, α = arctg a + πn, n Z;
ctgα = a, α = arcctg a + πn, n Z.
sin x = 1, x = π/2 + 2π, n Z; sin x = 0, x = πn, n Z;
cos x = 1, x = π + 2πn, n Z; cos x = 0, x = π/2 + πn, n Z; cos x = 1, x = 2πn, n Z;
arcsin(α) = arcsinα; arccos(α) = π arccosα; arctg(α) = arctgα; arcctg(α) = = πarcctgα;
. | . |
ex | ex+C |
sin x | cosx +C |
cos x | sinx + C |
sin(kx + b), | |
cos(kx+b), | |
tgx + C | |
−ctgx + C |
(i, j, k) , :
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A (x1; y1; z1); B (x2; y2; z2); :
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( ). La, Lb, Lc . : = :
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SΔ ; p ; hc
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MN . MN=0.5AC; MN║AC.
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