Ghi ch\u00fa: T\u00e0i li\u1ec7u tr\u00edch d\u1eabn<\/p>\n\n\n\n
H\u1ec7 s\u1ed1 g\u00f3c l\u00e0 m\u1ed9t trong nh\u1eefng ch\u01b0\u01a1ng tr\u00ecnh h\u1ecdc quan tr\u1ecdng c\u1ee7a To\u00e1n 10, 11. N\u1ebfu nh\u01b0 b\u1ea1n ch\u01b0a hi\u1ec3u r\u00f5 \u0111\u1ecbnh ngh\u0129a h\u1ec7 s\u1ed1 g\u00f3c l\u00e0 g\u00ec v\u00e0 c\u00f4ng th\u1ee9c t\u00ednh th\u00ec \u0111\u1eebng b\u1ecf l\u1ee1 c\u00e1c th\u00f4ng tin c\u00f3 trong b\u00e0i vi\u1ebft d\u01b0\u1edbi \u0111\u00e2y c\u1ee7a Vietlearn.org!<\/p>\n\n\n\n
H\u1ec7 s\u1ed1 g\u00f3c l\u00e0 g\u00ec? H\u1ec7 s\u1ed1 g\u00f3c c\u1ee7a \u0111\u01b0\u1eddng th\u1eb3ng l\u00e0 g\u00ec?<\/p>\n\n\n\n
Theo wikipedia, trong to\u00e1n h\u1ecdc h\u1ec7 s\u1ed1 g\u00f3c (\u0111\u1ed9 d\u1ed1c) l\u00e0 m\u1ed9t \u0111\u01b0\u1eddng th\u1eb3ng bi\u1ec3u di\u1ec5n \u0111\u1ed9 g\u1ed1c hay grat. Gi\u00e1 tr\u1ecb c\u1ee7a \u0111\u1ed9 d\u1ed1c c\u00e0ng cao th\u00ec \u0111\u1ed9 nghi\u00eang c\u1ee7a \u0111\u01b0\u1eddng th\u1eb3ng c\u00e0ng cao. \u0110\u1ed9 d\u1ed1c th\u01b0\u1eddng \u0111\u01b0\u1ee3c m\u00f4 t\u1ea3 l\u00e0 t\u1ec9 l\u1ec7 c\u1ee7a s\u1ef1 gia t\u0103ng gi\u1eefa 2 \u0111i\u1ec3m tr\u00ean tr\u1ee5c y c\u1ee7a \u0111\u01b0\u1eddng th\u1eb3ng chia cho s\u1ef1 gia t\u0103ng c\u1ee7a hai \u0111i\u1ec3m tr\u00ean tr\u1ee5c x c\u1ee7a \u0111\u01b0\u1eddng th\u1eb3ng \u0111\u00f3.<\/p>\n\n\n\n
C\u1ee5 th\u1ec3, h\u1ec7 s\u1ed1 g\u00f3c c\u1ee7a m\u1ed9t \u0111\u01b0\u1eddng th\u1eb3ng n\u1eb1m tr\u00ean m\u1eb7t ph\u1eb3ng ch\u1ee9a h\u1ec7 tr\u1ee5c t\u1ecda \u0111\u1ed9 x v\u00e0 y \u0111\u01b0\u1ee3c bi\u1ec3u di\u1ec5n b\u1eb1ng m. H\u1ec7 s\u1ed1 g\u00f3c n\u00e0y \u0111\u01b0\u1ee3c \u0111\u1ecbnh ngh\u0129a l\u00e0 s\u1ef1 thay \u0111\u1ed5i t\u1ecda \u0111\u1ed9 tr\u00ean tr\u1ee5 y chia cho s\u1ef1 thay \u0111\u1ed5i t\u1ecda \u0111\u1ed9 tr\u00ean tr\u1ee5c x, gi\u1eefa hai \u0111i\u1ec3m kh\u00e1c bi\u1ec7t c\u1ee7a \u0111\u01b0\u1eddng th\u1eb3ng. H\u1ec7 s\u1ed1 g\u00f3c \u0111\u01b0\u1ee3c bi\u1ec3u di\u1ec5n b\u1eb1ng ph\u01b0\u01a1ng tr\u00ecnh: m = = Tan (\u2205).<\/p>\n\n\n\n
Trong \u0111\u00f3: l\u00e0 s\u1ef1 thay \u0111\u1ed5i v\u1ecb tr\u00ed c\u1ee7a \u0111\u01b0\u1eddng th\u1eb3ng tr\u00ean hai tr\u1ee5c t\u1ecda \u0111\u1ed9 x v\u00e0 y.<\/p>\n\n\n\n
C\u00f9ng c\u00f3 m\u1ed9t \u0111\u1ecbnh ngh\u0129a kh\u00e1c \u0111\u01b0\u1ee3c \u0111\u01b0a ra \u0111\u1ec3 gi\u1ea3i th\u00edch kh\u00e1i ni\u1ec7m h\u1ec7 s\u1ed1 g\u00f3c l\u00e0 g\u00ec. Trong m\u1eb7t ph\u1eb3ng h\u1ec7 tr\u1ee5c t\u1ecda \u0111\u1ed9 Oxy, h\u1ec7 s\u1ed1 g\u00f3c c\u1ee7a m\u1ed9t \u0111\u01b0\u1eddng th\u1eb3ng (d) \u0111\u01b0\u1ee3c x\u00e1c \u0111\u1ecbnh l\u00e0 tan \u03b1. Trong \u0111\u00f3 \u03b1 ch\u00ednh l\u00e0 g\u00f3c \u0111\u01b0\u1ee3c t\u1ea1o b\u1edfi \u0111\u01b0\u1eddng th\u1eb3ng (d) c\u00f9ng v\u1edbi chi\u1ec1u d\u01b0\u01a1ng c\u1ee7a tr\u1ee5c Ox, t\u1eeb \u0111\u00f3 ta c\u00f3:<\/p>\n\n\n\n
N\u1ebfu g\u00f3c \u03b1 \u2260 90o, th\u00ec a = tan \u03b1 l\u00e0 h\u1ec7 s\u1ed1 g\u00f3c c\u1ee7a \u0111\u01b0\u1eddng th\u1eb3ng (d).<\/p>\n\n\n\n
N\u1ebfu nh\u01b0 a > 0 th\u00ec 0 < \u03b1 < 90\u00b0<\/p>\n\n\n\n
N\u1ebfu nh\u01b0 a < 0 th\u00ec 90\u00b0 < \u03b1 < 180\u00b0<\/p>\n\n\n\n
N\u1ebfu g\u00f3c \u03b1 = 90o (d\u22a5Ox) th\u00ec \u0111\u01b0\u1eddng th\u1eb3ng (d) kh\u00f4ng c\u00f3 h\u1ec7 s\u1ed1 g\u00f3c b\u1edfi g\u00f3c tan 90\u00b0 kh\u00f4ng x\u00e1c \u0111\u1ecbnh.<\/p>\n\n\n\n
M\u1ec7nh \u0111\u1ec1 1: Ph\u01b0\u01a1ng tr\u00ecnh \u0111\u01b0\u1eddng th\u1eb3ng (d) c\u00f3 h\u1ec7 s\u1ed1 g\u00f3c l\u00e0 a s\u1ebd c\u00f3 d\u1ea1ng y = ax + b<\/p>\n\n\n\n
M\u1ec7nh \u0111\u1ec1 2: \u0110\u01b0\u1eddng th\u1eb3ng (d) \u0111i qua \u0111i\u1ec3m M0 (x0;y0) v\u00e0 c\u00f3 h\u1ec7 s\u1ed1 g\u00f3c a c\u00f3 ph\u01b0\u01a1ng tr\u00ecnh l\u00e0 y = a (x\u2212x0)+y0<\/p>\n\n\n\n
Hai \u0111\u01b0\u1eddng th\u1eb3ng tr\u00f9ng nhau ho\u1eb7c song song s\u1ebd c\u00f3 c\u00f9ng m\u1ed9t h\u1ec7 s\u1ed1 g\u00f3c.<\/p>\n\n\n\n
H\u1ec7 s\u1ed1 g\u00f3c ti\u1ebfp tuy\u1ebfn l\u00e0 g\u00ec?<\/p>\n\n\n\n
Ti\u1ebfp tuy\u1ebfn c\u1ee7a \u0111\u1ed3 th\u1ecb m\u1ed9t h\u00e0m s\u1ed1 t\u1ea1i m\u1ed9t \u0111i\u1ec3m l\u00e0 m\u1ed9t \u0111\u01b0\u1eddng th\u1eb3ng ti\u1ebfp x\u00fac v\u1edbi \u0111\u1ed3 th\u1ecb h\u00e0m s\u1ed1 t\u1ea1i \u0111i\u1ec3m \u0111\u00f3. \u0110\u1ea1o h\u00e0m b\u1eadc nh\u1ea5t c\u1ee7a h\u00e0m s\u1ed1 t\u1ea1i ho\u00e0nh \u0111\u1ed9 c\u1ee7a \u0111i\u1ec3m, f \u2032 ( x 0 ) ch\u00ednh l\u00e0 h\u1ec7 s\u1ed1 g\u00f3c c\u1ee7a ti\u1ebfp tuy\u1ebfn.<\/p>\n\n\n\n
C\u00e1ch t\u00ednh h\u1ec7 s\u1ed1 g\u00f3c \u0111\u01b0\u1eddng th\u1eb3ng<\/p>\n\n\n\n
G\u00f3c t\u1ea1o b\u1edfi \u0111\u01b0\u1eddng th\u1eb3ng y =ax +b (a \u2260 0) v\u1edbi tr\u1ee5c Ox<\/p>\n\n\n\n
G\u1ecdi A l\u00e0 giao \u0111i\u1ec3m c\u1ee7a \u0111\u01b0\u1eddng th\u1eb3ng y = ax + b v\u1edbi tr\u1ee5c Ox. M l\u00e0 m\u1ed9t \u0111i\u1ec3m thu\u1ed9c \u0111\u01b0\u1eddng th\u1eb3ng, n\u1eb1m \u1edf ph\u00eda tr\u00ean tr\u1ee5c Ox. Khi \u0111\u00f3 l\u00e0 g\u00f3c t\u1ea1o b\u1edfi \u0111\u01b0\u1eddng th\u1eb3ng y = ax + b v\u1edbi tr\u1ee5c Ox.<\/p>\n\n\n\n
Tr\u01b0\u1eddng h\u1ee3p a > 0: a > 0, g\u00f3c t\u1ea1o b\u1edfi \u0111\u01b0\u1eddng th\u1eb3ng y = ax + b v\u00e0 tr\u1ee5c Ox s\u1ebd l\u00e0 g\u00f3c nh\u1ecdn v\u00e0 n\u1ebfu nh\u01b0 a c\u00e0ng l\u1edbn th\u00ec g\u00f3c \u0111\u00f3 c\u00e0ng l\u1edbn.<\/p>\n\n\n\n
Tr\u01b0\u1eddng h\u1ee3p a < 0: a < 0 g\u00f3c \u0111\u01b0\u1ee3c t\u1ea1o b\u1edfi \u0111\u01b0\u1eddng th\u1eb3ng y = ax + b v\u00e0 c\u00f3 tr\u1ee5c Ox l\u00e0 g\u00f3c t\u00f9 v\u00e0 n\u1ebfu a c\u00e0ng b\u00e9 th\u00ec g\u00f3c \u0111\u00f3 c\u00e0ng l\u1edbn.<\/p>\n\n\n\n
G\u00f3c t\u1ea1o b\u1edfi \u0111\u01b0\u1eddng th\u1eb3ng y = ax + b v\u00e0 tr\u1ee5c Ox s\u1ebd ph\u1ee5 thu\u1ed9c v\u00e0o h\u1ec7 s\u1ed1 a. Ng\u01b0\u1eddi ta g\u1ecdi a l\u00e0 h\u1ec7 s\u1ed1 g\u00f3c c\u1ee7a \u0111\u01b0\u1eddng th\u1eb3ng y = ax + b.<\/p>\n\n\n\n
Ch\u00fa \u00fd:<\/p>\n\n\n\n
Ta c\u00f3 \u0111i\u1ec3m A n\u1eb1m tr\u00ean tr\u1ee5c ho\u00e0nh n\u00ean y = 0 v\u00e0 x = . V\u1eady t\u1ecda \u0111\u1ed9 \u0111i\u1ec3m A l\u00e0 A(; 0) v\u00e0 \u0111\u1ed9 d\u00e0i \u0111o\u1ea1n OA =<\/p>\n\n\n\n
Ta c\u00f3 \u0111i\u1ec3m B n\u1eb1m tr\u00ean tr\u1ee5c tung n\u00ean x = 0 v\u00e0 y = b. V\u1eady t\u1ecda \u0111\u1ed9 \u0111i\u1ec3m B l\u00e0 B(0; b) v\u00e0 \u0111\u1ed9 d\u00e0i \u0111o\u1ea1n OB = |b|.<\/p>\n\n\n\n
a > 0: tan = = = =a<\/p>\n\n\n\n
T\u1eeb \u0111\u00f3 d\u00f9ng b\u1ea3ng l\u01b0\u1ee3ng gi\u00e1c ho\u1eb7c m\u00e1y t\u00ednh b\u1ecf t\u00fai suy ra s\u1ed1 \u0111o c\u1ee7a<\/p>\n\n\n\n
a < 0: tan (180\u00b0 \u2013 ) = tan = = = -a (do a < 0)<\/p>\n\n\n\n
T\u1eeb \u0111\u00f3 t\u00ecm s\u1ed1 \u0111o c\u1ee7a g\u00f3c (180\u00b0 -), sau \u0111\u00f3 suy ra .<\/p>\n\n\n\n
C\u00e1c \u0111\u01b0\u1eddng th\u1eb3ng c\u00f3 c\u00f9ng h\u1ec7 s\u1ed1 a (a l\u00e0 h\u1ec7 s\u1ed1 c\u1ee7a x) th\u00ec s\u1ebd t\u1ea1o v\u1edbi tr\u1ee5c Ox c\u00e1c g\u00f3c b\u1eb1ng nhau.<\/p>\n\n\n\n
Khi b = 0, ta c\u00f3 h\u00e0m s\u1ed1 y = ax, a l\u00e0 h\u1ec7 s\u1ed1 g\u00f3c c\u1ee7a \u0111\u01b0\u1eddng th\u1eb3ng y = ax<\/p>\n\n\n\n
M\u1ed9t s\u1ed1 b\u00e0i t\u1eadp h\u1ec7 s\u1ed1 g\u00f3c \u0111\u01b0\u1eddng th\u1eb3ng y= ax+b<\/p>\n\n\n\n
C\u00e2u 1: Cho h\u00e0m s\u1ed1 y = x + 2. T\u00ednh g\u00f3c t\u1ea1o b\u1edfi \u0111\u01b0\u1eddng th\u1eb3ng y = x + 2 v\u1edbi tr\u1ee5c Ox (l\u00e0m tr\u00f2n \u0111\u1ebfn ph\u00fat).<\/p>\n\n\n\n
G\u1ee3i \u00fd:<\/p>\n\n\n\n
T\u00ecm giao \u0111i\u1ec3m A gi\u1eefa \u0111\u01b0\u1eddng th\u1eb3ng y = x + 2 v\u1edbi tr\u1ee5c Ox.<\/p>\n\n\n\n
T\u00ecm giao \u0111i\u1ec3m B gi\u1eefa \u0111\u01b0\u1eddng th\u1eb3ng y = x + 2 v\u1edbi tr\u1ee5c Oy.<\/p>\n\n\n\n
V\u1ebd \u0111\u1ed3 th\u1ecb h\u00e0m s\u1ed1 y = x + 2<\/p>\n\n\n\n
\u0110\u1ed3 th\u1ecb h\u00e0m s\u1ed1 \u0111\u00e3 cho \u0111i qua hai \u0111i\u1ec3m A(0; 2); B(-2; 0)<\/p>\n\n\n\n
G\u1ecdi g\u00f3c t\u1ea1o b\u1edfi \u0111\u01b0\u1eddng th\u1eb3ng y = x + 2 v\u1edbi tr\u1ee5c Ox l\u00e0 \u03b1, ta c\u00f3 = \u03b1 X\u00e9t tam gi\u00e1c vu\u00f4ng OAB , ta c\u00f3 tan \u03b1= = = 1 (1 ch\u00ednh l\u00e0 h\u1ec7 s\u1ed1 g\u00f3c c\u1ee7a \u0111\u01b0\u1eddng th\u1eb3ng y = x + 2)<\/p>\n\n\n\n
Khi \u0111\u00f3 s\u1ed1 \u0111o g\u00f3c \u03b1 l\u00e0 \u03b1 = 45\u00b0<\/p>\n\n\n\n
C\u00e2u 2: Cho (d): y = ax + b. T\u00ecm a, b bi\u1ebft (d) \u0111i qua g\u1ed1c t\u1ecda \u0111\u1ed9 v\u00e0 song song v\u1edbi (d\u2019) trong \u0111\u00f3 (d\u2019) c\u00f3 h\u1ec7 s\u1ed1 g\u00f3c b\u1eb1ng 1.<\/p>\n\n\n\n
G\u1ee3i \u00fd \u0111\u00e1p \u00e1n<\/p>\n\n\n\n
Theo b\u00e0i ta, (d) \u0111i qua g\u1ed1c t\u1ecda \u0111\u1ed9 n\u00ean ta c\u00f3 b = 0<\/p>\n\n\n\n
(d) song song v\u1edbi (d\u2019) v\u00e0 (d\u2019) c\u00f3 h\u1ec7 s\u1ed1 g\u00f3c b\u1eb1ng 1 n\u00ean a = 1<\/p>\n\n\n\n
V\u1eady a = 1, b = 0.<\/p>\n\n\n\n
V\u1edbi c\u00e1c th\u00f4ng tin trong b\u00e0i vi\u1ebft \u201cH\u1ec7 s\u1ed1 g\u00f3c l\u00e0 g\u00ec? H\u1ec7 s\u1ed1 g\u00f3c c\u1ee7a \u0111\u01b0\u1eddng th\u1eb3ng l\u00e0 g\u00ec? L\u00fd thuy\u1ebft\u201d s\u1ebd gi\u00fap \u00edch b\u1ea1n. Truy c\u1eadp Vietlearn.org \u0111\u1ec3 t\u00ecm hi\u1ec3u nhi\u1ec1u th\u00f4ng tin h\u1eefu \u00edch kh\u00e1c, ch\u1eafc ch\u1eafn s\u1ebd gi\u00fap \u00edch b\u1ea1n r\u1ea5t nhi\u1ec1u \u0111\u00f3!<\/p>\n\n\n\n
<\/p>\n\n\n\n\n\n\n","protected":false},"excerpt":{"rendered":"
Ghi ch\u00fa: T\u00e0i li\u1ec7u tr\u00edch d\u1eabn H\u1ec7 s\u1ed1 g\u00f3c l\u00e0 m\u1ed9t trong nh\u1eefng ch\u01b0\u01a1ng tr\u00ecnh h\u1ecdc quan tr\u1ecdng c\u1ee7a To\u00e1n 10, 11. N\u1ebfu nh\u01b0 b\u1ea1n ch\u01b0a hi\u1ec3u r\u00f5 \u0111\u1ecbnh ngh\u0129a h\u1ec7 s\u1ed1 g\u00f3c l\u00e0 g\u00ec v\u00e0 c\u00f4ng th\u1ee9c t\u00ednh th\u00ec \u0111\u1eebng b\u1ecf l\u1ee1 c\u00e1c th\u00f4ng tin c\u00f3 trong b\u00e0i vi\u1ebft d\u01b0\u1edbi \u0111\u00e2y c\u1ee7a Vietlearn.org! H\u1ec7 […]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":"","_disable_autopaging":false},"categories":[1],"tags":[],"class_list":["post-4057","post","type-post","status-publish","format-standard","hentry","category-general"],"_links":{"self":[{"href":"https:\/\/www.vietlearn.org\/kien-thuc\/wp-json\/wp\/v2\/posts\/4057","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.vietlearn.org\/kien-thuc\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.vietlearn.org\/kien-thuc\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.vietlearn.org\/kien-thuc\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.vietlearn.org\/kien-thuc\/wp-json\/wp\/v2\/comments?post=4057"}],"version-history":[{"count":0,"href":"https:\/\/www.vietlearn.org\/kien-thuc\/wp-json\/wp\/v2\/posts\/4057\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.vietlearn.org\/kien-thuc\/wp-json\/wp\/v2\/media?parent=4057"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.vietlearn.org\/kien-thuc\/wp-json\/wp\/v2\/categories?post=4057"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.vietlearn.org\/kien-thuc\/wp-json\/wp\/v2\/tags?post=4057"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}