组卷网>知识点选题>三角恒等变换与平面向量结合问题
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3 . 在△ABC中,角ABC所对的边分别为abc,向量eqIda7608b72932b4abebacce21013a53e10 =(sinA,sinB),eqId9a1ad8b4a8c84db0bbbbabdc4847fc55 =(cosB,cosA),且eqIda7608b72932b4abebacce21013a53e10·eqId9a1ad8b4a8c84db0bbbbabdc4847fc55 = sin2C.
(1)求角C的大小;
(2)若sinA + sinB = 2sinC,且eqId47349746c1a84439aa91627ba310fd7a,求c的长度.
4 . 已知在平面直角坐标系中,eqId2efda802d5534f6d92d9f8af7aaec28b为坐标原点,定义非零向量eqId4126706d912b4533b4b7162b384abf44的“相伴函数”为eqId7910d6fd330f45c38664cc07ce3c99a6,向量eqId4126706d912b4533b4b7162b384abf44称为函数eqIdd3d2f823c2c64d1599a21edbafd401ac的“相伴向量”;记平面内所有向量的“相伴函数”构成的集合为eqId51d8a094ee99497ea839941c67407d85.
(1)已知eqIdf841e5c064a24d85ac95e716b806e99aeqId8fcd0ccbf2eb480fa8ca38f583a6ba34,若函数eqIdbf892314dab94cecb0472402956736e6为集合eqId51d8a094ee99497ea839941c67407d85中的元素,求其“相伴向量”的模的取值范围;
(2)已知点eqId38a73ac878314b8490313a1a5d5c6219满足条件:eqId278f4a80fb99455dbf9354b008329213eqIdd4c9be7fff674a048088044fcdaed538;若向量eqId868498ff9fa642879b7d44341bb0282c的“相伴函数”eqId9b37d03e47a347fc8fab9f814ba5fac4eqId02b4fd87b6dc469297673255c63eed1c处取得最大值,当eqIdaea992e70d4943e49e893817eb885ed7在区间eqIddd6aedb9b46d48c1974754d9abee9303变化时,求eqId5d0340ec8e6a4ae88e067690b9e1b04b的取值范围.
6 . 若向量eqId4b8848a4415e49689b2ad8bfa9037a84eqId2c9b49bf2f494ea4909e10b50f7c61af,其中eqId8ccf61601cf049d8a2100ee27d5b2419.记函数eqIdaa494fd123d9470d89ba0fd4b39bbfc4,若函数eqId6f13759e937144069819aed2ae5a1057的图象上相邻两个对称轴之间的距离是eqId2cb51764ae3949b9b698fc2f9527dff2
(1)写出函数eqId6f13759e937144069819aed2ae5a1057的解析式.
(2)若对任意eqId92044f1c239b415aa6e8f0074b35dee1eqIdd9d54d2e072142d9b444568e37eed77a恒成立,求实数m的取值范围.
(3)求实数a和正整数n,使得eqId6d6fffc3033d4348a401ad08433e3014eqIda9c249f466ac49e3a81d792f7553f12beqIde431abe484b74e29849c3347eb9a7553上恰有2021个零点.
7 . 已知eqId6fc94f6e181444c6b809fb393eb8fae6eqId3a06255e6f2c420594741082e049db02eqId539364e4c1e14718a3c9d34e7c7bb0b9
(1)记函数eqId87123333eff14f9e88735863b6b9009b,求函数eqId4837c94ef0ff4dcf9b1dda4df363275a取最大值时eqIda9cd3f94eb8045438f75e9daccfa7200的取值范围;
(2)求证:eqIda7608b72932b4abebacce21013a53e10eqId3985b92a5425427185a8498b7e29a964不平行;
(3)设eqId64b9b599fdb6481e9f8d9a94c102300b的三边eqId70a27b6ddf6b478285353abb3b1f3741eqIdaea992e70d4943e49e893817eb885ed7eqId44925af6fb19413689ba5616e3647cba满足eqId90edc9aab5b84946aca43933663c419f,且边eqIdaea992e70d4943e49e893817eb885ed7所对应的角为eqIda9cd3f94eb8045438f75e9daccfa7200,关于eqIda9cd3f94eb8045438f75e9daccfa7200的方程eqIdc14aad983fda4206a51ce4473b79da9d有且仅有一个实根,求实数eqId69f56ef2c88b4b73a560da59f5247a82的范围.
8 . 已知向量eqId94282a9f60a44f35a7f8b7796e0a203ceqIde749aa651da94665993f5854859167c4.
(1)若eqId2fabaf2ac696438aa5e0cf6be50c00d2,求eqIdf805b7e5ee9a476d85092aa17a92041c的值;
(2)若函数eqId0c2989037437496db43ddaff19ae411f,求此函数当eqIda247cabb0ebe48bb8ab8a495b7f2341c时的最大值.
9 . 已知eqId64b9b599fdb6481e9f8d9a94c102300b的外心为O,内心为.
说明: figure
(1)如图1,若eqId1e23be3e609e424cba88675d1d3da9e5.
①试用eqIdb85d53c455d14cd6a8dad6106e13e64c表示eqId3422767015a047cc85e220c7d49ec726
②求eqId0802bb2fc3f8440fa63a9db49982cd5b的值.
(2)如图2,若存在实数eqId5f420ef2d0b94c4b8a5d8e20a5d1ce2c,使eqId710d108072574c5386795aa18f70db17,试求eqId1688646d345a4fc9a20c11fe0284a0ee的值.
10 . 已知eqIdeb94068849a242f8b8ad9289c4feb2deeqId9822f9ed7e68437eb674d0d7b0da4de4,且eqIdfdec1c83f6e8424ab159be8e2ae1dc34
(1)求eqId4837c94ef0ff4dcf9b1dda4df363275aeqId73f4e2692ccf47c49da337b95ac3f8e1上的值域;
(2)已知eqId70a27b6ddf6b478285353abb3b1f3741eqIdaea992e70d4943e49e893817eb885ed7eqId44925af6fb19413689ba5616e3647cba分别为eqId64b9b599fdb6481e9f8d9a94c102300b的三个内角eqId052844cae8574a8ab842c38a039baac0eqId8754ce8cf7f34f04abb9a0c041f57f5ceqId19a4eb16029e4550a14f2afe4741a3c3对应的边长,若eqId5600675ffacb4e89a65a6ed7969c919f,且eqIddd4a5650f0b94c7cbb91b83107bfbc30eqId477da4034563424b98db6e75ea791554,求eqId64b9b599fdb6481e9f8d9a94c102300b的面积.
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