Belajar Trigonometri... :)

TRIGONOMETRI

Hal-hal yang perlu diingat:

sin α = y/r              cosec α = r/y

cos α = x/r             sec α = r/x

tan α = y/x             cot α = x/y

Fungsi trigonometri pada sudut istimewa

 

Sudut	00	300	450	600	900
Fungsi
sin α	0	½	½ √2	½ √3	1
cos α	1	½ √3	½ √2	½	0
tan α	0	1/3√3	1	√3	-
cosec α	1	2/3√3	√2	2	-
sec α	-	2	√2	2/3 √3	1
cot α	-	√3	1	1/3 √3	0

Fungsi Rumus Sudut Komplemen (penyiku)

sin (90 – α)⁰      = cos α⁰

cos (90 – α)⁰     = sin α⁰

tan (90 – α)⁰     = cot α⁰

cosec (90 – α)⁰ = sec α⁰

sec (90 – α)⁰     = cosec α⁰

cot (90 – α)⁰     = tan α⁰

contoh :

1.    sin 30⁰ = cos (90-60)⁰ = cos 60⁰

2.    cos 0⁰ = cos (90-90)⁰ = sin 90⁰

3.    tan 45⁰ = cos (90-45)⁰ = cot 45⁰

Rumus Sudut di Kuadran II

sin (90 + α)⁰     = cos α⁰

cos (90 + α)⁰    = – sin α⁰

tan (90 + α)⁰    = – cot α⁰

cosec (90 + α)⁰= sec α⁰

sec (90 + α)⁰    = – cosec α⁰

cot (90 + α)⁰    = – tan α⁰

contoh :

1.    sin 120⁰ = cos (90-30)⁰ = cos 30⁰

2.    cos 135⁰ = ─ sin (90-45)⁰ = ─ sin 45⁰

3.    tan 150⁰ =  ─ cot (90-60)⁰ = ─ cot 60⁰

sin (180 – α)⁰   = sin α⁰

cos (180 – α)⁰ = ─ cos α⁰

tan (180 – α)⁰   = ─ tan α⁰

cosec (180 – α)⁰= cosec α⁰

sec (180 – α)⁰   = ─ sec α⁰

cot (180 – α)⁰   = ─ cot α⁰

contoh :

1.    sin 120⁰ = sin (180-60)⁰ = sin 60⁰

2.    cos 135⁰ = ─ cos (180-45)⁰ = ─ cos 45⁰

3.    tan 150⁰ =  ─ tan (180-30)⁰ = ─ tan 30⁰

Rumus Sudut di Kuadran III

sin (180 + α)⁰ = ─ sin α⁰

cos (180 + α)⁰                 = ─ cos α⁰

tan (180 + α)⁰ = tan α⁰

cosec (180 + α)⁰= ─ cosec α⁰

sec (180 + α)⁰ = ─ sec α⁰

cot (180 + α)⁰ =  cot α⁰

contoh :

1.    sin 240⁰ = ─ sin (180 + 60)⁰ = ─ sin 60⁰

2.    cos 210⁰ = ─ cos (180 + 30)⁰ = ─ cos 30⁰

3.    tan 255⁰ = ─ tan (180 + 45)⁰ = tan 45⁰

sin (270 ─ α)⁰   = – cos α⁰

cos (270 ─ α)⁰ = – sin α⁰

tan (270 ─ α)⁰ = cot α⁰

cosec (270 ─ α)⁰ = – sec α⁰

sec (270 ─ α)⁰ = – cosec α⁰

cot (270 ─ α)⁰ = tan α⁰

contoh :

1.    sin 240⁰ = – cos (270 ─ 30)⁰ = – cos 30⁰

2.    cos 210⁰ = ─ sin (270 ─ 60)⁰ = ─ sin 60⁰

3.    tan 255⁰ =  cot (270 ─ 45)⁰ = cot 45⁰

Rumus Sudut di Kuadran IV

sin (270 + α)⁰ = ─ cos α⁰

cos (270 + α)⁰                 = sin α⁰

tan (270 + α)⁰ = ─ cot α⁰

cosec (270 + α)⁰= ─ sec α⁰

sec (270 + α)⁰ =  cosec α⁰

cot (270 + α)⁰ = ─ tan α⁰

sin (360 - α)⁰    = ─ sin α⁰

cos (360 - α)⁰   = cos α⁰

tan (360 - α)⁰    = ─tan α⁰

cosec (360 - α)⁰= ─ cosec α⁰

sec (360 - α)⁰    =  sec α⁰

cot (360 - α)⁰    = ─ cot α⁰

Rumus Sudut Negatif

sin (─α)⁰             = ─ sin α⁰

cos (─α)⁰            = cos α⁰

tan (─α)⁰            = ─tan α⁰

cosec (─α)⁰       = ─ cosec α⁰

sec (─α)⁰            =  sec α⁰

cot (─α)⁰            = ─ cot α⁰

contoh :

1.    sin (─30)⁰ = ─ sin 30⁰

2.    cos 330⁰ = sin (270 - 60)⁰ = sin 60⁰

3.    cos 330⁰ = cos (360 - 30)⁰ = cos 30⁰

4.  tan 315⁰ = ─ cot (270 - 45)⁰ = ─ cot 45⁰

5.  tan 315⁰ = ─ tan (360 - 45)⁰ = ─ tan 45⁰

^{sumber : Matematika SMA}