Trigonometri :)

PERBANDINGAN TRIGONOMETRI (sinus , cosinus , dn tangen)

sin * = depan/miring , kebalikan.ny cosecan (cosec) = miring/depan
cos * = samping/miring , kebalikan.ny secan (sec) = miring/samping
tan * = depan/samping , kebalikan.ny cotangen (cot) = samping/depan

Identitas Trigonometri
NB = ^ :: pangkat 2
/ :: per

cos^ * + sin^ * = 1
sec * = 1/cos *
cosec * = 1/sin *
tan * = sin * / cos *
1 + tan^ * = sec^ *
1 + cotan^ * = cosec^ *
cot^ * + 1 = cosec^ *

Sudut Sudut Istimewa
V = akar
~ = tdk terdefinisi
sin ::
0 = 0
30 = 1/2
45 = 1/2 V2
60 = 1/2 V3
90 = 1

cos ::
0 = 1
30 = 1/2 V3
45 = 1/2 V2
60 = 1/2
90 = 0

tan ::
0 = 0
30 = 1/3 V3
45 = 1
60 = V3
90 = ~

cosec ::
0 = ~
30 = 2
45 = V2
60 = 2/V3
90 = 1

sec ::
0 = 1
30 = 2/V3
45 = V2
60 = 2
90 = ~

cot ::
0 = ~
30 = V3
45 = 1
60 = 1/V3
90 = 0

Sudut Sudut Berelasi
' = derajat
1) Kuadran I (0' < * < 90' ) :: semua positif
90' - *
sin (90 - *) = cos * cosec (90 - *) = sec *
cos (90 - *) = sin * sec (90 - *) = cosec *
tan (90 - *) = cot * cot (90 - *) = tan *

2) Kuadran II :: hnya sin yng positif
﹑ 90 + *
sin (90 + * ) = cos * cosec (90 + *) = sec *
cos (90 + * ) = -sin * sec (90 + *) = -cosec *
tan (90 + *) = -cot * cot (90 + *) = -tan *
﹑180 - *
sin (180 - *) = sin* cosec (180 - *) = cosec *
cos (180 - *) = -cos* sec(180 - *) = -sec *
tan (180 - *) = -tan* cot(180 - *) = -cotan *

3) Kuadran III :: hnya tan yng positif
﹑ 180 + *
sin (180 + *) = -sin* cosec (180 + *) = -cosec *
cos (180 + *) = -cos* sec(180 + *) = -sec *
tan (180 + *) = tan* cot(180 + *) = cotan *

﹑270 - *
sin (270 - *) = -cos * cosec (270 - *) = -sec *
cos (270 - *) = -sin * sec (270 - *) = -cosec *
tan (270 - *) = cot * cot (270 - *) = tan *

4) Kuadran IV :: hnya cos yng positif
﹑ 360 - *
sin (360 - *) = -sin* cosec (360 - *) = -cosec *
cos (360 - *) = cos* sec(360 - *) = sec *
tan (360 - *) = -tan* cot(360 - *) = -cotan *

﹑ 270 + *

sin (270 + *) = -cos * cosec (270 + *) = -sec *
cos (270 + *) = sin * sec (270 + *) = cosec *
tan (270 + *) = -cot * cot (270 + *) = -tan *

Rumus Rumus Segitiga dalam TRIGONOMETRI
1) aturan sinus
a/sinA = b/sinB = c/sinC
2) aturan cosinus
untuk sembarang segitiga ABC , berlaku ::
a^ = b^ + c^ - 2.b.c. Cos A
b^ = a^ + c^ - 2.a.c. Cos B
c^ = a^ + b^ - 2.a.b. Cos C

untuk menghitung besar sudut segitiga jika diketahui panjang ketiga sisinya , d.gunakan aturan cosinus sbb ::
cos A = b^ + c^ - a^/2.b.c
cos B = a^ + c^ - b^/2.a.c
cos C = a^ + b^ - c^/2.a.b

Luas Segitiga
1) Luas segitiga jika d.ketahui dua sisi dan satu sudut
L = 1/2 .b.c . Sin A
= 1/2 .a.c. Sin B
= 1/2 .a.b. Sin C
2) luas segitiga jika diketahui dua sudut dan satu sisi
L = a^ . Sin B . Sin C / 2.sin (B + C)
= b^ . Sin A . Sin C / 2.sin (A + C)
= c^ . Sin A . Sin B / 2.sin (A+B)
3) luas segitiga jika diketahui ketiga sisi.ny
L = Vs (s-a) (s-b) (s-c)
s = 1/2 (a+b+c) = 1/2 keliling
4) Luas segi-n beraturan
n/2 . r^ . Sin 360/n