[r]
Trang 1CC CÆNG THÙC L×ÑNG GIC
1 CUNG V GÂC L×ÑNG GIC
1.1 Radian v ë
10= π
1800 π
1.2 Mi·n gi¡ trà cõa c¡c gi¡ trà l÷ñng gi¡c
−1 ≤ sin α ≤ 1 ∀α ∈ R −∞ ≤ cot a ≤ +∞ ∀α 6= kπ
−1 ≤ cos α ≤ 1 ∀α ∈ R −∞ ≤ tan a ≤ +∞ ∀α 6= π2 + kπ
1.3 D§u cõa c¡c gi¡ trà l÷ñng gi¡c
Gi¡ trà l÷ñng gi¡c\Ph¦n t÷ I II III IV
1.4 Gi¡ trà l÷ñng gi¡c cõa c¡c cung gâc °c bi»t
α a0 0 00 π6 300 π4 450 π3 600 π2 900
√ 2 2
√ 3
2 1
√ 3 2
√ 2 2
1
2 0
3 1 √3 k
3 0
2 MËT SÈ CÆNG THÙC L×ÑNG GIC.
sin2α + cos2α = 1 tan α cot α = 1
tan α = sin α
cos α cot α =
cos α sin α
1 + tan2α = 1
cos2α 1 + cot
2α = 1 sin2α
Trang 22.2 Cung li¶n k¸t
Cung (gâc) èi Cung (gâc) bò Cung (gâc) phö Cung (gâc) hìn k²mπ
cos (−α) = cos α sin (π − α) = sin α cos
π
2 − α
= sin α tan (π + α) = tan α
sin (−α) = − sin α cos (π − α) = − cos α sinπ
2 − α
= cos α cot (π + α) = cot α
tan (−α) = − tan α tan (π − α) = − tan α tan
π
2 − α
= cot α sin (π + α) = − sin α
cot (−α) = − cot α cot (π − α) = − cot α cotπ
2 − α
= tan α cos (π + α) = − cos α
Quy tc nhî : "cos èi, sin bò, phö ch²o, kh¡c π tan"
2.3 Cæng thùc cëng
Cæng thùc cëng
cos (a + b) = cos a cos b − sin a sin b cos (a − b) = cos a cos b + sin a sin b
sin (a + b) = sin a cos b + sin b cos a sin (a − b) = sin a cos b − sin b cos a
tan (a + b) = tan a + tan b
1 − tan a tan b tan (a − b) =
tan a − tan b
1 + tan a tan b
2.4 Cæng thùc nh¥n æi
Cæng thùc nh¥n æi sin 2a = 2 sin a cos a cos 2a = cos2a − sin2a = 2 cos2a − 1 = 1 − 2 sin2a
tan 2a = 2 tan a
1 − tan2a
2.5 Cæng thùc h¤ bªc
Cæng thùc h¤ bªc cos2a = 1+cos 2a2
sin2a = 1−cos 2a2
tan2a = 1−cos 2a1+cos 2a
Trang 32.6 Cæng thùc bi¸n êi t½ch th nh têng
Cæng thùc bi¸n êi t½ch th nh têng
cos a cos b = 1
2[cos (a + b) + cos (a − b)]
sin a sin b = −1
2[cos (a + b) − cos (a − b)]
sin a cos b = 1
2[sin (a + b) + sin (a − b)]
2.7 Cæng thùc bi¸n êi têng th nh t½ch
Cæng thùc bi¸n êi têng sang t½ch
cos a + cos b = 2 cos a + b
2
cos a − b
2
cos a − cos b = −2 sin a + b
2
sin a − b 2
sin a + sin b = 2 sin a + b
2
cos a − b
2
sin a − sin b = 2 cos a + b
2
sin a − b
2