ÔĶÁÏÂÁвÄÁÏ£¬²¢½â¾öºóÃæµÄÎÊÌ⣮

ÔÚÈñ½Ç¡÷ABCÖУ¬¡ÏA¡¢¡ÏB¡¢¡ÏCµÄ¶Ô±ß·Ö±ðÊÇa¡¢b¡¢c£®¹ýA×÷AD¡ÍBCÓÚD(Èçͼ)£¬

ÔòsinB=£¬sinC=£¬¼´AD=csinB£¬AD=bsinC£¬ÓÚÊÇcsinB=bsinC£¬¼´£®

ͬÀíÓУ¬£®

ËùÒÔ¡­¡­¡­(*)

¼´£ºÔÚÒ»¸öÈý½ÇÐÎÖУ¬¸÷±ßºÍËüËù¶Ô½ÇµÄÕýÏҵıÈÏàµÈ£®

(1)ÔÚÈñ½ÇÈý½ÇÐÎÖУ¬ÈôÒÑÖªÈý¸öÔªËØa¡¢b¡¢¡ÏA£¬ÔËÓÃÉÏÊö½áÂÛ(*)ºÍÓйض¨Àí¾Í¿ÉÒÔ

Çó³öÆäÓàÈý¸öδ֪ԪËØc¡¢¡ÏB¡¢¡ÏC£¬ÇëÄã°´ÕÕÏÂÁв½ÖèÌî¿Õ£¬Íê³ÉÇó½â¹ý³Ì£º

¡¡¡¡µÚÒ»²½£ºÓÉÌõ¼þa¡¢b¡¢¡ÏA ¡¡¡¡¡¡¡¡¡ÏB£»

¡¡¡¡µÚ¶þ²½£ºÓÉÌõ¼þ ¡ÏA¡¢¡ÏB£® ¡¡¡¡¡¡¡¡¡ÏC£»

¡¡¡¡µÚÈý²½£ºÓÉÌõ¼þ£®¡¡¡¡¡¡¡¡ ¡¡¡¡¡¡¡¡ c£®

(2)Ò»»õÂÖÔÚC´¦²âµÃµÆËþAÔÚ»õÂֵı±Æ«Î÷30¡ãµÄ·½ÏòÉÏ£¬Ëæºó»õÂÖÒÔ28£®4º£ÀʱµÄËٶȰ´±±Æ«¶«45¡ãµÄ·½Ïòº½ÐУ¬°ëСʱºóµ½´ïB´¦£¬´ËʱÓÖ²âµÃµÆËþAÔÚ»õÂֵı±Æ«Î÷70¡ãµÄ·½ÏòÉÏ(Èçͼ)£¬Çó´Ëʱ»õÂÖ¾àµÆËþAµÄ¾àÀëAB(½á¹û¾«È·µ½0£®1£®²Î¿¼Êý¾Ý£ºsin40¡ã=0.643£¬sin65¡ã=0.906£¬sin70¡ã=0.940£¬sin75¡ã=0.966)£®

Á·Ï°²áϵÁдð°¸
Ïà¹ØÏ°Ìâ

¿ÆÄ¿£º³õÖÐÊýѧ À´Ô´£º ÌâÐÍ£ºÔĶÁÀí½â

ÔĶÁÏÂÁвÄÁÏ£¬²¢½â¾öºóÃæµÄÎÊÌ⣬ÔÚÈñ½Ç¡÷ABCÖУ¬¡ÏA¡¢¡ÏB¡¢¡ÏCµÄ¶Ô±ß·Ö±ðÊÇa¡¢b¡¢c£¬Ôò
£¨1£©¹ýµãA×÷AD¡ÍBCÓÚD£¨Èçͼ1£©£¬
ÔòÔÚRt¡÷ABDÖУ¬AD=
 
£»£¨ÏÞÓÃa¡¢b¡¢c¡¢¡ÏA¡¢¡ÏB¡¢¡ÏCÖеÄÔªËØÀ´±íʾ£©
ÔÚRt¡÷ACDÖУ¬AD=
 
£»
¡à
 
=
 

¡à
 
=
 

ͬÀí×îºó¿ÉµÃ£¬
 
=
 
=
 
£»
£¨2£©Óó߹滭¡÷ABCµÄÍâ½ÓÔ²¡ÑO£¬°ë¾¶Îªr£¨Í¼2£©£¬ÇëÄãÁíÓò»Í¬µÄ·½·¨Ö¤Ã÷ÒÔÉϽáÂÛ£»²¢Ð´³öÉÏÊö½áÂÛÓë¡÷ABCÍâ½ÓÔ²Ö±¾¶µÄ¹Øϵ£®
£¨3£©Ó¦Ó㺡÷ABCÖУ¬Èô¡ÏA=30¡ã£¬¡ÏB=45¡ã£¬b=
2
£¬Ôòa=
 
£¬Íâ½ÓÔ²°ë¾¶r=
 
£®
¾«Ó¢¼Ò½ÌÍø

²é¿´´ð°¸ºÍ½âÎö>>

¿ÆÄ¿£º³õÖÐÊýѧ À´Ô´£º ÌâÐÍ£ºÔĶÁÀí½â

¾«Ó¢¼Ò½ÌÍøÔĶÁÏÂÁвÄÁÏ£¬²¢½â¾öºóÃæµÄÎÊÌ⣮
ÔÚÈñ½Ç¡÷ABCÖУ¬¡ÏA¡¢¡ÏB¡¢¡ÏCµÄ¶Ô±ß·Ö±ðÊÇa¡¢b¡¢c£®¹ýA×÷AD¡ÍBCÓÚD£¨Èçͼ£©£¬ÔòsinB=
AD
c
£¬sinC=
AD
b
£¬¼´AD=csinB£¬AD=bsinC£¬ÓÚÊÇcsinB=bsinC£¬
¼´
b
sinB
=
c
sinC
£®Í¬ÀíÓÐ
c
sinC
=
a
sinA
£¬
a
sinA
=
b
sinB
£®
ËùÒÔ
a
sinA
=
b
sinB
=
c
sinC
¡­£¨*£©
¼´£ºÔÚÒ»¸öÈý½ÇÐÎÖУ¬¸÷±ßºÍËüËù¶Ô½ÇµÄÕýÏҵıÈÏàµÈ£®
£¨1£©ÔÚÈñ½ÇÈý½ÇÐÎÖУ¬ÈôÒÑÖªÈý¸öÔªËØa¡¢b¡¢¡ÏA£¬ÔËÓÃÉÏÊö½áÂÛ£¨*£©ºÍÓйض¨Àí¾Í¿ÉÒÔÇó³öÆäÓàÈý¸öδ֪ԪËØc¡¢¡ÏB¡¢¡ÏC£¬ÇëÄã°´ÕÕÏÂÁв½ÖèÌî¿Õ£¬Íê³ÉÇó½â¹ý³Ì£º
µÚÒ»²½£ºÓÉÌõ¼þa¡¢b¡¢¡ÏA
ÓùØϵʽ
 
Çó³ö
¡ÏB£»
µÚ¶þ²½£ºÓÉÌõ¼þ¡ÏA¡¢¡ÏB
ÓùØϵʽ
 
Çó³ö
¡ÏC£»
µÚÈý²½£ºÓÉÌõ¼þ
 
ÓùØϵʽ
 
Çó³ö
c£®
£¨2£©Èçͼ£¬ÒÑÖª£º¡ÏA=60¡ã£¬¡ÏC=75¡ã£¬a=6£¬ÔËÓÃÉÏÊö½áÂÛ£¨*£©ÊÔÇób£®

²é¿´´ð°¸ºÍ½âÎö>>

¿ÆÄ¿£º³õÖÐÊýѧ À´Ô´£º ÌâÐÍ£ºÔĶÁÀí½â

ÔĶÁÏÂÁвÄÁÏ£¬²¢½â¾öºóÃæµÄÎÊÌ⣮
ÔÚÈñ½Ç¡÷ABCÖУ¬¡ÏA¡¢¡ÏB¡¢¡ÏCµÄ¶Ô±ß·Ö±ðÊÇa¡¢b¡¢c£®¹ýA×÷AD¡ÍBCÓÚD£¨Èçͼ£©£¬ÔòsinB=
AD
c
£¬sinC=
AD
b
£¬¼´AD=csi¾«Ó¢¼Ò½ÌÍønB£¬AD=bsinC£¬ÓÚÊÇcsinB=bsinC£¬¼´
b
sinB
=
c
sinC
£®
ͬÀíÓÐ
c
sinC
=
a
sinA
£¬
a
sinA
=
b
sinB
£®
ËùÒÔ
a
sinA
=
b
sinB
=
c
sinC
¡­£¨*£©
¼´£ºÔÚÒ»¸öÈý½ÇÐÎÖУ¬¸÷±ßºÍËüËù¶Ô½ÇµÄÕýÏҵıÈÏàµÈ£®
£¨1£©ÔÚÈñ½ÇÈý½ÇÐÎÖУ¬ÈôÒÑÖªÈý¸öÔªËØa¡¢b¡¢¡ÏA£¬ÔËÓÃÉÏÊö½áÂÛ£¨*£©ºÍÓйض¨Àí¾Í¿ÉÒÔ
Çó³öÆäÓàÈý¸öδ֪ԪËØc¡¢¡ÏB¡¢¡ÏC£¬ÇëÄã°´ÕÕÏÂÁв½ÖèÌî¿Õ£¬Íê³ÉÇó½â¹ý³Ì£º
µÚÒ»²½£ºÓÉÌõ¼þa¡¢b¡¢¡ÏA
ÓùØϵʽ
 
Çó³ö
¡ÏB£»
µÚ¶þ²½£ºÓÉÌõ¼þ¡ÏA¡¢¡ÏB£®
ÓùØϵʽ
 
Çó³ö
¡ÏC£»
µÚÈý²½£ºÓÉÌõ¼þ£®
 
ÓùØϵʽ
 
Çó³ö
c£®
£¨2£©Ò»»õ»õÂÖÔÚC´¦²âµÃµÆËþAÔÚ»õÂֵı±Æ«Î÷30¡ãµÄ·½ÏòÉÏ£¬Ëæºó»õÂÖÒÔ28.4º£Àï/ʱµÄËٶȰ´±±Æ«¶«45¡ãµÄ·½Ïòº½ÐУ¬°ëСʱºóµ½´ïB´¦£¬´ËʱÓÖ²âµÃµÆËþAÔÚ»õÂֵı±Æ«Î÷70¡ãµÄ·½ÏòÉÏ£¨Èçͼ£©£¬Çó´Ëʱ»õÂÖ¾àµÆËþAµÄ¾àÀëAB£¨½á¹û¾«È·¾«Ó¢¼Ò½ÌÍøµ½0.1£®²Î¿¼Êý¾Ý£ºsin40¡ã=0.643£¬sin65¡ã=0.90 6£¬sin70¡ã=0.940£¬sin75¡ã=0.966£©£®

²é¿´´ð°¸ºÍ½âÎö>>

¿ÆÄ¿£º³õÖÐÊýѧ À´Ô´£º ÌâÐÍ£ºÔĶÁÀí½â

ÔĶÁÏÂÁвÄÁÏ£¬²¢½â¾öºóÃæ¸ø³öµÄÎÊÌâ
Àý£®¸ø¶¨¶þ´Îº¯Êýy=£¨x-1£©2+1£¬µ±t¡Üx¡Üt+1ʱ£¬ÇóyµÄº¯ÊýÖµµÄ×îСֵ£®
½â£ºº¯Êýy=£¨x-1£©2+1£¬Æä¶Ô³ÆÖá·½³ÌΪx=1£¬¶¥µã×ø±êΪ£¨1£¬1£©£¬Í¼Ï󿪿ÚÏòÉÏ£®ÏÂÃæ·ÖÀàÌÖÂÛ£º

£¨1£©Èçͼ1Ëùʾ£¬Èô¶¥µãºá×ø±êÔÚ·¶Î§t¡Üx¡Üt+1×ó²àʱ£¬¼´ÓÐ1£¼t£®´ËʱyËæxµÄÔö´ó¶øÔö´ó£¬µ±x=tʱ£¬º¯ÊýÈ¡µÃ×îСֵ£¬y×îСֵ=(t-1)2+1£»
£¨2£©Èçͼ2Ëùʾ£¬Èô¶¥µãºá×ø±êÔÚ·¶Î§t¡Üx¡Üt+1ÄÚʱ£¬¼´ÓÐt¡Ü1¡Üt+1£¬½âÕâ¸ö²»µÈʽ£¬¼´0¡Üt¡Ü1£®´Ëʱµ±x=1ʱ£¬º¯ÊýÈ¡µÃ×îСֵ£¬y×îСֵ=1£»
£¨3£©Èçͼ3Ëùʾ£¬Èô¶¥µãºá×ø±êÔÚ·¶Î§t¡Üx¡Üt+1ÓÒ²àʱ£¬ÓÐt+1£¼1£¬½â²»µÈʽ¼´µÃt£¼0£®´ËʱYËæXµÄÔö´ó¶ø¼õС£¬µ±x=t+1ʱ£¬º¯ÊýÈ¡µÃ×îСֵ£¬y×îСֵ=t2+1
×ÛÉÏÌÖÂÛ£¬µ±1£¼tʱ£¬º¯ÊýÈ¡µÃ×îСֵ£¬y×îСֵ=(t-1)2+1£®
´Ëʱµ±0¡Üt¡Ü1ʱ£¬º¯ÊýÈ¡µÃ×îСֵ£¬y×îСֵ=1£®
µ±t£¼0ʱ£¬º¯ÊýÈ¡µÃ×îСֵ£¬y×îСֵ=t2+1
¸ù¾ÝÉÏÊö²ÄÁÏ£¬Íê³ÉÏÂÁÐÎÊÌ⣺
ÎÊÌ⣺Çóº¯Êýy=x2+2x+3ÔÚt¡Üx¡Üt+2ʱµÄ×îСֵ£®

²é¿´´ð°¸ºÍ½âÎö>>

¿ÆÄ¿£º³õÖÐÊýѧ À´Ô´£º ÌâÐÍ£ºÔĶÁÀí½â

¹Û²ìÓë˼¿¼£ºÔĶÁÏÂÁвÄÁÏ£¬²¢½â¾öºóÃæµÄÎÊÌâ
ÔÚÈñ½Ç¡÷ABCÖУ¬¡ÏA¡¢¡ÏB¡¢¡ÏCµÄ¶Ô±ß·Ö±ðÊÇa¡¢b¡¢c£¬¹ýA×÷AD¡ÍBCÓÚD£¨Èçͼ£¨1£©£©£¬ÔòsinB=
AD
c
£¬sinC=
AD
b
£¬¼´AD=csinB£¬AD=bsinC£¬ÓÚÊÇcsinB=bsinC£¬¼´
b
sinB
=
c
sinC
£¬Í¬ÀíÓУº
c
sinC
=
a
sinA
£¬
a
sinA
=
b
sinB
£¬
ËùÒÔ
a
sinA
=
b
sinB
=
c
sinC
£®
¼´£ºÔÚÒ»¸öÈý½ÇÐÎÖУ¬¸÷±ßºÍËüËù¶Ô½ÇµÄÕýÏҵıÈÏàµÈÔÚÈñ½ÇÈý½ÇÐÎÖУ¬ÈôÒÑÖªÈý¸öÔªËØ£¨ÖÁÉÙÓÐÒ»Ìõ±ß£©£¬ÔËÓÃÉÏÊö½áÂÛºÍÓйض¨Àí¾Í¿ÉÒÔÇó³öÆäÓàÈý¸öδ֪ԪËØ£®
¸ù¾ÝÉÏÊö²ÄÁÏ£¬Íê³ÉÏÂÁи÷Ì⣮

£¨1£©Èçͼ£¨2£©£¬¡÷ABCÖУ¬¡ÏB=45¡ã£¬¡ÏC=75¡ã£¬BC=60£¬Ôò¡ÏA=
60¡ã
60¡ã
£»AC=
20
6
20
6
£»
£¨2£©×Ô´ÓÈ¥ÄêÈÕ±¾Õþ¸®×ÔÖ÷×Ôµ¼¡°µöÓ㵺¹úÓл¯¡±ÄÖ¾çÒÔÀ´£¬ÎÒ¹úÕþ¸®Áé»îÓ¦¶Ô£¬ÏÖÈç½ñÒѶԵöÓ㵺ִÐг£Ì¬»¯Ñ²Âߣ®Ä³´ÎѲÂßÖУ¬Èçͼ£¨3£©£¬ÎÒÓæÕþ204´¬ÔÚC´¦²âµÃAÔÚÎÒÓæÕþ´¬µÄ±±Æ«Î÷30¡ãµÄ·½ÏòÉÏ£¬ËæºóÒÔ40º£Àï/ʱµÄËٶȰ´±±Æ«¶«30¡ãµÄ·½Ïòº½ÐУ¬°ëСʱºóµ½´ïB´¦£¬´ËʱÓÖ²âµÃµöÓ㵺AÔڵı±Æ«Î÷75¡ãµÄ·½ÏòÉÏ£¬Çó´ËʱÓæÕþ204´¬¾àµöÓ㵺AµÄ¾àÀëAB£®£¨½á¹û¾«È·µ½0.01£¬
6
¡Ö2.449
£©

²é¿´´ð°¸ºÍ½âÎö>>

ͬ²½Á·Ï°²á´ð°¸