Page 19 - E-BOOK PASTI LOLOS TPS SNBT 2024_Neat

Beberapa rumus/identitas trigonometri : sin(270 o − α = −cos α
)
sinα cos(270 o − α = −sin α
)
tanα= sin α + cos α = 1
2
2
cosα tan(270 o − α = cot α
)
2
2
−
cosα sin α= 1 cos α
cotα= • Kuadran IV :
sinα cos α= 1 sin α
−
2
2
)
1 2 2 sin(360 o − α = −sin α
+
cosecα= sec α= 1 tan α
)
sinα 2 2 cos(360 o − α = cos α
+
1 cosec α= 1 cot α tan(360 o − α = −tan α
)
secα= sin(−α = − sinα
)
cosα sin(270 o +α = −cos α
)
=
1 cos(−α ) cosα o
)
cotα= cos(270 +α = sin α
)
tanα tan(−α = − tanα tan(270 o +α = −cot α
)
Ukuran sudut dapat dituliskan dengan
satuan derajat atau radian dengan rumus C. ATURAN SINUS, COSINUS, DAN LUAS
1
o
π = radian 180 dan 1 = π radian . SEGITIGA
o
180
Berikut tabel nilai trigonometri sudut Perhatikan gambar segitiga ABC berikut.
istimewa (kuadran 1).
0° = 0π 30° =π/3 45° = π/4 60° = π/3 90° = π/2
1 1 1
sin α 0 2 3 1
2 2 2
1 1 1
cos α 1 3 2 0
2 2 2 Pada sembarang segitiga ABC, berlaku
1 rumus berikut.
tan 0 3 1 3 ∞
3 a b c
• Aturan sinus : = =
sinA sinB sinC
B. SUDUT-SUDUT BERELASI • Aturan cosinus :
• Kuadran II : 2 =a 2 +b 2 − c ⋅ 2bc cosA
)
sin(180 o − α = sin α 2 =b 2 + a 2 − c ⋅ 2ac cosB
)
cos(180 o − α = −cos α 2 = c 2 + a 2 −b ⋅ 2ab cosC
tan(180 o − α = −tan α
)
• Luas segitiga :
)
sin(90 o +α = cos α
1
)
cos(90 o +α = −sin α L ∆ =ABC ⋅ ac sinB
2
tan(90 o +α = −cot α 1
)
= bc ⋅sinA
• Kuadran III : 2
1
)
sin(180 +α = −sin α = ab ⋅sinC
2
cos(180 +α = −cos α
)
)
tan(180 +α = + tan α
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