TUYỂN TẬP 20 ĐỀ THI KHẢO SÁT HỌC SINH GIỎI MÔN TIẾNG ANH LỚP 6 NĂM 2020 (CÓ Đ...
Nm3 trigonometria formulario
1. FORMULARIO
seno = cateto opuesto / hipotenusa
coseno = cateto contiguo / hipotenusa
tangente = c. opuesto / c. adyacente
cosec = hipotenusa / cateto opuesto
sec = hipotenusa / cateto contiguo
cotg = cateto contiguo / cateto opuesto
cosec α = 1 / sen α
sec α = 1 / cos α
cotg α = 1 / tg α
tg α = sen α / cos α
cotg α = cos α / sen α
sin(-x) = -sin(x)
csc(-x) = -csc(x)
cos(-x) = cos(x)
sec(-x) = sec(x)
tan(-x) = -tan(x)
cot(-x) = -cot(x)
tan(x+- y) = (tan x+- tan y) / (1-+ tan x tan y)
sin(2x) = 2 sin x cos x
cos(2x) = cos^2(x) - sin^2(x) = 2 cos^2(x) - 1 = 1 - 2 sin^2(x)
tan(2x) = 2 tan(x) / (1 - tan^2(x))
sin^2(x) = 1/2 - 1/2 cos(2x)
cos^2(x) = 1/2 + 1/2 cos(2x)
sin x - sin y = 2 sin( (x - y)/2 ) cos( (x + y)/2 )
cos x - cos y = -2 sin( (x-y)/2 ) sin( (x + y)/2 )
c^2 = a^2 + b^2 - 2ab cos(C)
b^2 = a^2 + c^2 - 2ac cos(B)
a^2 = b^2 + c^2 - 2bc cos(A)
sen
cos
tg
cosec
sec
cotg
0º
0
1
0
--1
---
30º
1/2
3/2
3/3
2/1
2/3
3/3
sen 2 α+ cos 2 α = 1
1 + cotg 2 α = cosec 2 α
45º
2/2
2/2
1
2/2
2/2
1
60º
3/2
1/2
3
2/3
2
1/3
90º
1
0
--1
--0
tg 2 α + 1 = sec 2 α
SUMA Y DIFERENCIA
sen (a + b) = sen a · cos b + cos a · sen b
sen (a - b) = sen a · cos b - cos a · sen b
2. cos (a + b) = cos a · cos b - sen a · sen b
tg a + tg b
tg(a + b) =
1 − tg a • tg b
cos (a - b) = cos a · cos b + sen a · sen b
tg(a − b) =
tg a − tg b
1 + tg a • tg b
ANGULOS DOBLE Y MITAD
sen 2a = 2 sen a · cos a
2 tg a
tg 2a = 1 − tg 2 a
1 − cos 2a
2
cos a = ±
1 + cos 2a
2
tg a = ±
cos 2a = cos2 a - sen2 a
sen a = ±
1 − cos 2a
1 + cos 2a
PRODUCTOS Y SUMAS
sen a · cos b =
1
{sen (a + b) + sen (a 2
b)}
1
{sen (a + b) - sen (a - b)}
2
1
cos a · cos b =
{cos (a + b) + cos (a 2
cos a · sen b =
sen A + sen B = 2 sen
A+B
A−B
sen
2
2
A+B
A−B
cos A + cos B = 2 cos
cos
2
2
sen A − sen B = 2 cos
b)}
1
sen a · sen b =
{cos (a + b) - cos (a - b)}
2
A+B
A−B
cos
2
2
cos A − cos B = −2 sen
A+B
A−B
sen
2
2