初中三角函数专题

初中三角 函数 excel方差函数excelsd函数已知函数     2 f x m x mx m      2 1 4 2拉格朗日函数pdf函数公式下载 专 题 快递公司问题件快递公司问题件货款处理关于圆的周长面积重点题型关于解方程组的题及答案关于南海问题 第一讲 222b1、勾股定理:直角三角形两直角边、的平方和等于斜边的平方。 a，b,cac 2、如下图，在Rt?ABC中，?C为直角，则?A的锐角三角函数为(?A可换成?B): 定 义 表达式 取值范围 关 系 ，A的对边a0,sinA,1 正 sinA,cosB sinA,sinA, c弦 (?A为锐角) 斜边cosA,sinB 22b，A的邻边0,cosA,1 余 sinA，cosA,1 cosA,cosA, c斜边弦 (?A为锐角) tanA,cotB a，A的对边tanA,0正 tanA,tanA, cotA,tanB b，A的邻边切 (?A为锐角) 1(倒数) tanA,cotAbcotA,0，A的邻边余 cotA,cotA, tanA,cotA,1 a，A的对边切 (?A为锐角) 3、任意锐角的正弦值等于它的余角的余弦值;任意锐角的余弦值等于它的余角的正弦值。 B 由，A，，B,90:sinA,cosBsinA,cos(90:,A) 对斜边 cosA,sin(90:,A)cosA,sinB得，B,90:,，A c a边 b A C 邻边 4、任意锐角的正切值等于它的余角的余切值;任意锐角的余切值等于它的余角的正切值。 tanA,cotB 由，A，，B,90:tanA,cot(90:,A) cotA,tanB cotA,tan(90:,A) 得，B,90:,，A 5、0?、30?、45?、60?、90?特殊角的三角函数值(重要) 三角函数 0? 30? 45? 60? 90? 213 sin, 01 222 213 cos, 10222 3 tan, 30 1 -3 3 cot, 3-1 03 6、正弦、余弦的增减性: ,,,,, 当0???90?时，sin随的增大而增大，cos随的增大而减小。 7、正切、余切的增减性: used in the gray primary elevation on bread, about the size of 50mm square, vertical and horizontal spacing by about 1.5M. To ash cakes after water will not collapse, then brushing with water/cement ratio for 0.4~0.5 at the grass-roots of cement slurry with layers, start paving mortar, if ash cakes has hardened, with mortar laying with leveling and knocking ash cake, filled with mortar. With Darby ash cake height mortar, scrape, rub wood trowel flat. Wooden trowel evenly back operation. Depending on the temperature level the screed is complete 24h, begin to water conservation, water per day and three days before 2~4, watered every day and night 1~2, curing time of not less than 7d. Required pavement surface should not have cracks, peeling, pitted and phenomena such as sand, skirting works closely with wall stickers ... Spike access fee, so as not to destroy the waterproof layer. Strengthen the quality inspection of onion part during the construction, highlighting the ground onion, drain, drain, sanitary ware and other peripheral waterproof layer must not touch losses component shall not be modified. (F) the exterior Windows of Windows and doors project this project uses aluminum alloy Windows, residential entry door to door, other doors installed by the owners themselves. Window and door installation position: outside the door in the wall, outside the window in the wall. 1, preparation: after installation 当0?<<90?时，tan随的增大而增大，cot随的增大而减小。 ,,,,, 1、解直角三角形的定义:已知边和角(两个，其中必有一边)?所有未知的边和角。 222依据:?边的关系:;?角的关系:A+B=90?;?边角关系:三角函数的定义。a，b,c (注意:尽量避免使用中间数据和除法) 2、应用举例: (1)仰角:视线在水平线上方的角;俯角:视线在水平线下方的角。 视线铅垂线 水平线仰角ihl,:h俯角 α视线l hhlii,(2)坡面的铅直高度和水平宽度的比叫做坡度(坡比)。用字母表示，即。坡度一般l1:mi,1:5写成的形式，如等。 hi,,tan,把坡面与水平面的夹角记作(叫做坡角)，那么。 ,l 3、从某点的指北方向按顺时针转到目标方向的水平角，叫做方位角。如图3，OA、OB、OC、OD的方向角分别是:45?、135?、225?。 4、指北或指南方向线与目标方向 线所成的小于90?的水平角，叫做方向角。如图4,OA、OB、OC、OD的方向角分别是:北偏东30?(东北方向) ， 南偏东45?(东南方向)， 南偏西60?(西南方向)， 北偏西60?(西北方向)。 第28章 《锐角三角函数》 一、选择题 41. 若为锐角,,,,且，则为　　　　　　　　　,( ) sintan 5 9334 ABCD(　　 (　　 (　　 (25543 2(在Rt?ABC中，?C = 90?，下列式子不一定成立的是( ) A(sinA = sinB B(cosA=sinB C(sinA=cosB D(?A+?B=90? 3(直角三角形的两边长分别是6，8，则第三边的长为( ) 72A(10 B(2 C(10或2 D(无法确定 4(在Rt?ABC中，?C=90?，当已知?A和a时，求c，应选择的关系式是( ) aaa A(c = B(c = C(c = a?tanA D(c = sinAcosAtanA ses aluminum alloy Windows, residential entry door to door, other doors installed by the owners themselves. Window and door iject uf layer must not touch losses component shall not be modified. (F) the exterior Windows of Windows and doors project this proonion part during the construction, highlighting the ground onion, drain, drain, sanitary ware and other peripheral waterprooon of s closely with wall stickers ... Spike access fee, so as not to destroy the waterproof layer. Strengthen the quality inspectinot less than 7d. Required pavement surface should not have cracks, peeling, pitted and phenomena such as sand, skirting workme of omplete 24h, begin to water conservation, water per day and three days before 2~4, watered every day and night 1~2, curing timortar, scrape, rub wood trowel flat. Wooden trowel evenly back operation. Depending on the temperature level the screed is cking ash cake, filled with mortar. With Darby ash cake height roots of cement slurry with layers, start paving mortar, if ash cakes has hardened, with mortar laying with leveling and knoc-apse, then brushing with water/cement ratio for 0.4~0.5 at the grassash cakes after water will not coll used in the gray primary elevation on bread, about the size of 50mm square, vertical and horizontal spacing by about 1.5M. Tonstallation position: outside the door in the wall, outside the window in the wall. 1, preparation: after installation2 ,,5、的值等于( ) sin45，cos45 3，1A. B. C. D. 1 322 6(在Rt?ABC中，?C=90?，tan A=3，AC等于10，则S?ABC等于( ) 50A. 3 B. 300 C. D. 15 3 (当锐角α>30?时，则cosα的值是( ) 7 1133 A(大于 B(小于 C(大于 D(小于 22228(小明沿着坡角为30?的坡面向下走了2米，那么他下降( ) 23 A(1米 B(3米 C(23 D( 3 9(如图，在四边形ABCD中，?A=60?，?B=?D=90?，BC=2，CD=3，则AB=( ) 8323(A)4 (B)5 (C) (D) 3 410(已知Rt?ABC中，?C=90?，tanA=，BC=8，则AC等于( ) 3 32 A(6 B( C(10 D(12 3二、填空题 11(计算2sin30?+2cos60?+3tan45?=_______( 12(若sin28?=cosα，则α=________( 13(已知?ABC中，?C=90?，AB=13，AC=5，则tanA=______( 3(某坡面的坡度为1:14，则坡角是_______度( 415(在?ABC中，?C,90?，AB,10cm，sinA,，则BC的长为_______cm. 5 30:C45:16.如图，在高楼前点测得楼顶的仰角为，向高楼前进60米到点，又测得仰角为，D 则该高楼的高度大约为 A.82米 B.163米 C.52米 D.70米 17(如图，小鸣将测倾器安放在与旗杆AB底部相距6m的C处，量出测倾器的高度CD,1m， ,测得旗杆顶端B的仰角,60?，则旗杆AB的高度为 ((计算结果保留根号) A 45:30: DBC (16题) (17题) ( 三、解答题 第7 题) wners ws and doors project this project uses aluminum alloy Windows, residential entry door to door, other doors installed by the ond other peripheral waterproof layer must not touch losses component shall not be modified. (F) the exterior Windows of Windoware arengthen the quality inspection of onion part during the construction, highlighting the ground onion, drain, drain, sanitary a such as sand, skirting works closely with wall stickers ... Spike access fee, so as not to destroy the waterproof layer. Stnomenday and night 1~2, curing time of not less than 7d. Required pavement surface should not have cracks, peeling, pitted and phe erature level the screed is complete 24h, begin to water conservation, water per day and three days before 2~4, watered everytemp ortar. With Darby ash cake height mortar, scrape, rub wood trowel flat. Wooden trowel evenly back operation. Depending on thelayers, start paving mortar, if ash cakes has hardened, with mortar laying with leveling and knocking ash cake, filled with m roots of cement slurry with-ash cakes after water will not collapse, then brushing with water/cement ratio for 0.4~0.5 at the grasssed in the gray primary elevation on bread, about the size of 50mm square, vertical and horizontal spacing by about 1.5M. To uon: after installationthemselves. Window and door installation position: outside the door in the wall, outside the window in the wall. 1, preparati3 18(由下列条件解直角三角形:在Rt?ABC中，?C=90?: (1)已知a=4，b=8， (2)已知b=10，?B=60?( (3)已知c=20，?A=60?. (4) (2)已知a=5，?B=35? 19(计算下列各题( 22cos30cos60:，:22(1)sin30?+cos45?+2sin60??tan45?; (2)+ sin45? tan60tan30:，: 四、解下列各题 20(如图所示，平地上一棵树高为5米，两次观察地面上的影子，•第一次是当阳光与地面成45?时，第二次是阳光与地面成30?时，第二次观察到的影子比第一次长多少米, 21(如图，AB是江北岸滨江路一段，长为3千米，C为南岸一渡口，•为了解决两岸交通困难，拟在渡口C处架桥(经测量得A在C北偏西30?方向，B在C的东北方向，从C处连接两岸的最短的桥长多少,(精确到0.1) nstallation position: outside the door in the wall, outside the window in the wall. 1, preparation: after installationses aluminum alloy Windows, residential entry door to door, other doors installed by the owners themselves. Window and door iject uf layer must not touch losses component shall not be modified. (F) the exterior Windows of Windows and doors project this proonion part during the construction, highlighting the ground onion, drain, drain, sanitary ware and other peripheral waterprooon of s closely with wall stickers ... Spike access fee, so as not to destroy the waterproof layer. Strengthen the quality inspectinot less than 7d. Required pavement surface should not have cracks, peeling, pitted and phenomena such as sand, skirting workme of omplete 24h, begin to water conservation, water per day and three days before 2~4, watered every day and night 1~2, curing timortar, scrape, rub wood trowel flat. Wooden trowel evenly back operation. Depending on the temperature level the screed is cking ash cake, filled with mortar. With Darby ash cake height roots of cement slurry with layers, start paving mortar, if ash cakes has hardened, with mortar laying with leveling and knoc-apse, then brushing with water/cement ratio for 0.4~0.5 at the grassash cakes after water will not coll used in the gray primary elevation on bread, about the size of 50mm square, vertical and horizontal spacing by about 1.5M. To4 答案: a1(D 2(A 3(C [点拨]长为8的边即可能为直角边，也可能为斜边(4(A [点拨]sinA=，c a所以c=( sinA 35(A 6(D 7(D [点拨]余弦值随着角度的增大而减小，α>30?，cos30?=，所以2 3cosa<( 2 BCBC88(A 9(B 10(A [点拨]tanA=，AC==6( ,4ACtanA 3 133311( 4+ [点拨]原式=2×+2×+3×1=4+( 12( 62? 22 12BC122222ABAC,135,13( [点拨]BC===12，tanA==( 55AC 1314( 30? [点拨]坡角α的正切tanα=，所以α=30?( ,33 15( 8 16. 82米 17. (63，1)m 22225ab，,，4818(解:(1)c= =4; bb10103在Rt,ABC中，a, (2)==，,0tanBtan6033b1010203c= , ,,,sinsin603B:3 2 ?A=90?-?B=90?-60?=30? a such as sand, skirting works closely with wall stickers ... Spike access fee, so as not to destroy the waterproof layer. Stnomenday and night 1~2, curing time of not less than 7d. Required pavement surface should not have cracks, peeling, pitted and phe erature level the screed is complete 24h, begin to water conservation, water per day and three days before 2~4, watered everytemp ortar. With Darby ash cake height mortar, scrape, rub wood trowel flat. Wooden trowel evenly back operation. Depending on thelayers, start paving mortar, if ash cakes has hardened, with mortar laying with leveling and knocking ash cake, filled with m roots of cement slurry with-ash cakes after water will not collapse, then brushing with water/cement ratio for 0.4~0.5 at the grasssed in the gray primary elevation on bread, about the size of 50mm square, vertical and horizontal spacing by about 1.5M. To uon: after installationthemselves. Window and door installation position: outside the door in the wall, outside the window in the wall. 1, preparatiwners ws and doors project this project uses aluminum alloy Windows, residential entry door to door, other doors installed by the ond other peripheral waterproof layer must not touch losses component shall not be modified. (F) the exterior Windows of Windoware arengthen the quality inspection of onion part during the construction, highlighting the ground onion, drain, drain, sanitary 5 13 (3)a = c×sinA=20×=10，b=c×cos60?=10×=5(?B=90?-?A=90?-60?322 =30? 111336622219(解:(1)原式=()+()+××1=++=+ 224242222 3122()()，2222 (2)原式=+=1+ 2233，3 20(第一次观察到的影子长为5×cot45?=5(米);第二次观察到的影子长为5•×cot30? =53(米)( 3两次观察到的影子长的差是5-5米( 21(过点C作CD?AB于点D( CD就是连接两岸最短的桥(设CD=x米( 在直角三角形BCD中，?BCD=45?，所以BD=CD=x( 3 在直角三角形ACD中，?ACD=30?，所以AD=CD×tan?ACD=x?tan30?=x( 3 3933,因为AD+DB=AB，所以x+x=3，x=?1.9(米) 32 nstallation position: outside the door in the wall, outside the window in the wall. 1, preparation: after installationses aluminum alloy Windows, residential entry door to door, other doors installed by the owners themselves. Window and door iject uf layer must not touch losses component shall not be modified. (F) the exterior Windows of Windows and doors project this proonion part during the construction, highlighting the ground onion, drain, drain, sanitary ware and other peripheral waterprooon of s closely with wall stickers ... Spike access fee, so as not to destroy the waterproof layer. Strengthen the quality inspectinot less than 7d. Required pavement surface should not have cracks, peeling, pitted and phenomena such as sand, skirting workme of omplete 24h, begin to water conservation, water per day and three days before 2~4, watered every day and night 1~2, curing timortar, scrape, rub wood trowel flat. Wooden trowel evenly back operation. Depending on the temperature level the screed is cking ash cake, filled with mortar. With Darby ash cake height roots of cement slurry with layers, start paving mortar, if ash cakes has hardened, with mortar laying with leveling and knoc-apse, then brushing with water/cement ratio for 0.4~0.5 at the grassash cakes after water will not coll used in the gray primary elevation on bread, about the size of 50mm square, vertical and horizontal spacing by about 1.5M. To6