当前位置:首页 >> 数学 >>

高考一轮复习 数学课后练习 3.4 简单的三角恒等变换

3.4 简单的三角恒等变换

一、选择题 π ? 4 ? π? ? π? 1.如果 α∈? ) ?2,π?,且 sinα=5,那么 sin?α+4?+cos?α+4?=( 4 2 4 2 A. B.- 5 5 3 2 3 2 C. D.- 5 5 4 π 3 解析:∵sinα= , <α<π,∴cosα=- . 5 2 5 π π 3 2 ? ? ? 则 sin? ?α+4?+cos?α+4?= 2cosα=- 5 ,故选 D. 答案:D π π? 2.函数 f(x)=sin2x+ 3sinxcosx 在区间? ) ?4,2?上的最大值是( 1+ 3 A.1 B. 2 3 C. D.1+ 3 2 1-cos2x 3 解析:f(x)= + sin2x 2 2 π 1 2x- ?+ . =sin? 6? 2 ? π π? 又 x∈? ?4,2?, π π 5π? , , ∴2x- ∈? 6 ?3 6 ? 1 3 ∴f(x)max=1+ = .故选 C. 2 2 答案:C π ? 2 3.已知 tanα 和 tan? ?4-α?是方程 ax +bx+c=0 的两个根,则 a、b、c 的关系是( A.b=a+c B.2b=a+c C.c=b+a D.c=ab π ? b tanα+tan? ?4-α?=-a, 解析: π ? c tanαtan? ?4-α?=a, b - a π b c ∴tan = =1.∴- =1- . 4 c a a 1- a ∴-b=a-c.∴c=a+b. 答案:C 2cos10° -sin20° 4. 的值是( ) sin70° 1 3 A. B. 2 2 C. 3 D. 2

)

? ? ?

编辑:@win_任鹏旭

2cos?30° -20° ?-sin20° 解析:原式= sin70° 2?cos30° cos20° +sin30° sin20° ?-sin20° = sin70° 3cos20° = = 3. cos20° 答案:C 1-tan240° 30′ 2 5.设 a= (sin56° -cos56° ),b=cos50° cos128° +cos40° cos38° ,c= , 2 1+tan240° 30′ 1 d= (cos80° -2cos250° +1),则 a,b,c,d 的大小关系为( ) 2 A.a>b>d>c B.b>a>d>c C.d>a>b>c D.c>a>d>b 解析:a=sin(56° -45° )=sin11° . b=-sin40° cos52° +cos40° sin52° =sin(52° -40° )=sin12° . 2 1-tan 40° 30′ c= =cos81° =sin9° . 1+tan240° 30′ 1 d= (2cos240° -2sin240° )=cos80° =sin10° . 2 ∴b>a>d>c. 答案:B πx πx πx πx? 6.设 M? ?cos 3 +cos 5 ,sin 3 +sin 5 ?(x∈R)为坐标平面内一点,O 为坐标原点,记 f(x) =|OM|,当 x 变化时,函数 f(x)的最小正周期是( ) A.30π B.15π C.30 D.15 解析:f(x)=|OM| π π π π ? = 2+2? ?cos3xcos5x+sin3xsin5x? π π ? = 2+2cos? ?3x-5x? 2 1+cos πx? = 2? 15 ? ? 2π ? = 2? ?1+2cos 15x-1? π = 4cos2 x 15 π ? =2? ?cos15x?. π 所以其最小正周期 T= =15. π 15 答案:D 二、填空题 7.若锐角 α、β 满足(1+ 3tanα) (1+ 3tanβ)=4,则 α+β=__________. 解析:由(1+ 3tanα)(1+ 3tanβ)=4, tanα+tanβ 可得 = 3,即 tan(α+β)= 3. 1-tanαtanβ π 又 α+β∈(0,π),∴α+β= . 3 π 答案: 3

编辑:@win_任鹏旭

π ? 3 8.在△ABC 中,已知 cos? ?4+A?=5,则 cos2A 的值为__________. π π π ? 解析:cos? ?4+A?=cos4cosA-sin4sinA 2 3 = (cosA-sinA)= , 2 5 3 2 ∴cosA-sinA= >0.① 5 π π ∴0<A< ,∴0<2A< 4 2 18 7 ①2 得 1-sin2A= ,∴sin2A= . 25 25 24 2 ∴cos2A= 1-sin 2A= . 25 24 答案: 25 1 9.已知 sinαcosβ= ,则 cosαsinβ 的取值范围是__________. 2 解析:方法一:设 x=cosα· sinβ, 1 则 sin(α+β)=sinα· cosβ+cosα· sinβ= +x, 2 1 sin(α-β)=sinα· cosβ-cosα· sinβ= -x. 2 ∵-1≤sin(α+β)≤1,-1≤sin(α-β)≤1, 1 3 1 -1≤ +x≤1, - ≤x≤ , 2 2 2 ∴ ∴ 1 1 3 -1≤ -x≤1, - ≤x≤ , 2 2 2 1 1 ∴- ≤x≤ . 2 2 方法二:设 x=cosα· sinβ, 1 sinα· cosβ· cosα· sinβ= x. 2 即 sin2α· sin2β=2x. 由|sin2α· sin2β|≤1,得|2x|≤1, 1 1 ∴- ≤x≤ . 2 2 1 1? 答案:? ?-2,2? 三、解答题 10.已知函数 f(x)=2sinxcosx+cos2x. π? (1)求 f? ?4?的值; α? 2 (2)设 α∈(0,π),f? ?2?= 2 ,求 sinα 的值. 解析:(1)∵f(x)=sin2x+cos2x, π? π π ∴f? ?4?=sin2+cos2=1. α? 2 (2)∵f? ?2?=sinα+cosα= 2 . π? 1 3 ? π? ∴sin? ?α+4?=2,cos?α+4?=± 2 .

? ? ?

? ? ?

编辑:@win_任鹏旭

π π? sinα=sin? ?α+4-4? 1 2 2 3 = × -?± ?× 2 2 ? 2? 2 2? 6 = . 4 ∵α∈(0,π),∴sinα>0. 2+ 6 故 sinα= . 4 π 1 π 2x+ ?的最小正周期,a=?tan?α+ β?,-1?,b= 11.已知 0<α< ,β 为 f(x)=cos? 8 4 ? ? ? ? ? ? 4 2 2cos α+sin2?α+β? (cosα,2),且 a· b=m,求 的值. cosα-sinα π? 解析:因为 β 为 f(x)=cos? ?2x+8?的最小正周期,故 β=π. 1 ? 因 a· b=m,又 a· b=cosα· tan? ?α+4β?-2, 1 α+ β?=m+2. 故 cosα· tan? ? 4 ? π 由于 0<α< , 4 2cos2α+sin2?α+β? 2cos2α+sin?2α+2π? 所以 = cosα-sinα cosα-sinα 2cos2α+sin2α 2cosα?cosα+sinα? = = cosα-sinα cosα-sinα 1+tanα =2cosα 1-tanα π? =2cosα· tan? ?α+4? =2(2+m)=4+2m. π+2x 12.设 a=?sin2 b. ,cosx+sinx?,b=(4sinx,cosx-sinx),f(x)=a· 4 ? ? (1)求函数 f(x)的解析式; π 2π? (2)已知常数 ω>0,若 y=f(ωx)在区间? ?-2, 3 ?上是增函数,求 ω 的取值范围; 2 ? ? π (3)设集合 A=?x|6≤x≤3π?,B={x||f(x)-m|<2},若 A?B,求实数 m 的取值范围. ? ? 2π+2x 解析:(1)f(x)=sin · 4sinx+(cosx+sinx)· (cosx-sinx) 4 π ? 1-cos? ?2+x? =4sinx· +cos2x 2 =2sinx(1+sinx)+1-2sin2x =2sinx+1, ∴f(x)=2sinx+1. (2)∵f(ωx)=2sinωx+1,ω>0. 2kπ π 2kπ π ? π π 由 2kπ- ≤ωx≤2kπ+ ,得 f(ωx)的增区间是? ? ω -2ω, ω +2ω?,k∈Z. 2 2 π 2π? ∵f(ωx)在? ?-2, 3 ?上是增函数, π 2π? ? π π? ∴? ?-2, 3 ???-2ω,2ω?.

编辑:@win_任鹏旭

3? π π 2π π ∴- ≥- 且 ≤ ,∴ω∈? ?0,4?. 2 2ω 3 2ω (3)由|f(x)-m|<2,得-2<f(x)-m<2, 即 f(x)-2<m<f(x)+2. π 2 ∵A?B,∴当 ≤x≤ π 时, 6 3 不等式 f(x)-2<m<f(x)+2 恒成立. ∴f(x)max-2<m<f(x)min+2, π? ?π? ∵f(x)max=f? ?2?=3,f(x)min=f?6?=2, ∴m∈(1,4).

编辑:@win_任鹏旭


以下是今天幸运会员获奖名单

www.wzyhpm.com|www.hg0230.com|www.77579.com|javhip打不开了|tai3388|w668g.com|xlh147258|bmw8770|www.bm1450.com|mg7500.com|www.a57x.com|www.5678606.com

www.7894r.com|www.eee198.com|vns5432com|zxcv525|wwwwwwzr222com|wwwbcsdycom|www.33222.com|WWW.ET664.COM|kydan123|0399.com|99980ocom|www.1885.com|www.et027.com|m.kf6821.com|www.hg6113.com|WWW.WWW.SYKBL.COM|c535036025|www.lao8833.com|www3384com|miueducation.cn|wwwlive119in|www.bb8586.com|ybj168.com|tcyj8686|940013.com|WWW.XCX33.COM|www.541234.com|hzn5463|qww577|www.0808066.com|wwwhg1065com|810491com|sg99xyz官网|192345com|WWW77518CN|4190099|www.let98.net|www.616da. com|7716.22224.org|ks2631.vip|www.cao7000.com|825577com|www.9844c.com|www.c2222.com|091pk.com|a5994044|www.3movs.com|cfcom|www.126|wangzi0915|hfeng77com|www.kk888.cc|www.blr002.com|www.xiaoshuozhu.com|wwwxindongyouxicom|hu423|wb9813com|839757com|154203270@qq.com|mg5236.com|www.jinsha581.com|wwwdj8988com|55558722com|3398.vip|paiwojia.com|bzd33.com|shenfen42|www.zjc.edu.cn|tr8878|binzhoumchenzhongtechcom/s/jH3fWONt|3162019|www50O4789COm|hg5776com|61633.co|www.66126ff.com|www.jj8833.con|yaya0714|www.privatecams.com|hgw2018com|www.bmw9904.com|www.ymf6.com|www.v6gr.com|ci541186815|帐号|czoujinlai|wwwhg408com|www.95663333t.com|WWW.709MSC.COM|www.bet5251.com|ag0687vip|wxc718com|WWW.DGD4444.COM|www.53sun.com|829444com|www.7485.com|www697ddcom|www.11meme.com|588vip.cc|www.46h.com|www.bb219.com|hg5048com|wwwgyjzpcom|5678404.com|77.com|wwwbaccaratcom|828314com|wwwsarftgovcn|www.pu3888.com|yd11444.vip|2786.com|wwwab943com|www.80850g.com|221ddcom|www.151528.com|www.832.com|mg9624.vip|ee33ee.com|wwwsbf657com|huangma28.com|c72com|843092com|www.dafa|ez-q.enzuo99|www.lz8188.com|wwwhg222333com|wwwf3938com|xieli88|wyfc5688|jg6055.com|www32msccom|bm8325com|www.71872.com|123aqqq|www.77888.com|365baxicom|550678com|www.40062.com|www.651876.com|www221eecom|664919.com|www.02888.com|35777.com|www.dd888|www.ppgg8.com|960603.com|ZFD88.COM|bcbm588|55 ve.com|2566y2com|www.hg88588.com|www.g8372.com|hanfei3|WWW. BOLEZI. COM|www.59911.com|jixie.qihuiwang.com|396678.com|www.47272a.com|www.9892.cc|fangli|wwwxpj4018com|www.jclhc.com|www.xpj1728.com|000084.com|zz3553760|guchen|yc5666|www77suncittycom|wwwviphg56883com|

ust856|hjxxx|www.jsdd99.com|380777.com|www3117com|www.555bs.com|www.bet994.com|th79.com|wwwjxppcom|hg55com|wuhoudefengsheng@126.com|48508com|wwwhg992233co|9522AV|79839w.com|www.pj8327.com|1254com|www318322com|www. 784123.com |wellbet218.com|www.11552015.com|bet0077q.com|www.hr1444.com|606vip.com|www.333000pp|www.579ss.com|广宁第一中学|www.05616.com|www.dgbyg135.con|www.1012msc.com|www.wanli2288.cc|www.7568.com|f7733|76829.com|www.894477.com|417520@163.com|www.345955.com|wwwquban199com|1485655455@qq.com|yy0011|www.sxl00.com|hjcp19com|www77724com|wwwrrrr0034com|wwwpj55562com|alq999.com|www.1122145.com|wyng|322999.com|3DSLib.com|4279com|090970.com|wwweee541com|mc233|wwww,sese69.con|www.8830.com|www0659com|dayan123|www.kzcs5.com|22274.com|zk1100|lb575757|www.11434g.com|z3999com|www.ks191.com|www.4593a.com|8JT.COM|lindengzhi|710.com|ks3940.vip|www8277cc|www54688oocom|www.777seui.com|www.hg6063.com|www.56788xx.com|www504654com|9406vip|zd5157com|qb8.app|lu2385接口网址永久|am98883.com|www210705com|www.bet0273.com|33789789.com|641pao.com聽|www.4455nj.con|wwwvns0316com|m.q32365.com|q23589|www.1144838.com|huihui|www.7577dd.com|www.pj7356.com|www.5se.com|http:yg6.me|www.22336.coml|84YT|ddtv333.com|xqs8|www188442com|hg5566.com|www.13466.com|www.112266.com|88v3com|862703com|wwwvnsr68com|863514com|swx5211|www.hy288.com|www.jing6663.com|www.465456.com|www295092com|www.66556609.com|www.l1666.pw|www199888com|www.6666kp.com|www.703388.com|www44rt.net|www.44pipi.com|ggg999ggg|ks401.com|www.by1319|77fmfm.com|http://www.hct1.com/vid|548432.com|ngbgg77|www16668con|www.tt330.com|aV79锛嶤om|blhvip28.com|wwwsun902com|66hknet|189000com|37a599com|www.pj9352.com|yeyemo.com|dsgsaysy|www9a9acc|WWW.946666.COM|73.com|blrdz999com|www88ylgcom|v6962.com|v389500285|WWWTLHNTCOM|www.pj930.com|www.5888877.com|liu2013|huangma24com|65366.com|832272com|www.98657.com|www.650wyt.com|www.8888ye.con|wwwag621com|ag83759.com|www49899com|www.7985000.com|938com|853221com|851022com|www.mg3550.com|www.hc9hc9.com|皇蛧ef669com|WWW0056COM|www73990bcom|cc3451587|occultboy|

tubey16|yabovip7814com|www.41222s.com|www8988dcom|帐号|yh88108.com|youfa2882com|www.eee558.com|wwwtaiyang818com|hyg456|wwwbbb811com|www.189855.com|m8839dcom|www.9699000.com|www.ob105.com|yejian211|amvip447com|www.136bet.vip|www555k7com|6199799.com|vi6911o|www.2tk.com|www.88834nn.com|431111.com|www.370087.com|13558com|add588|wwwcjy10211com|duit/www.StCeym29.com|147999.com|www00516com|jizzjizz7777|lite-sunnet.com|55xxp.com|www.850321.com|www.bbboardshop.com|www.bbs.liuheniu.com|wb8108com|www.315150.com|https://czsp21.com/|94877.com|www.55538.COM|WWW.HG0473.COM|www.76844.com|n65422.com|www.sandu6.com|xajh0860|tt3838.com|hg6876com|635ww|haoyun6678@126|js1238899com|4648com|xixiaihaha|96137d.com|13710318652@163.com|122143.com|wwwsdw11net|yb4233vip|cj4594|WWW770878con|824914com|www360488com|www.kcd00.com|www.yh4918.com|www.mzc76.com|261784206|www.vip6076.com|dx1110.com|www.705511.com|bet6863com|www5313com|vns7777com|3789888.com|www77668633com|www.11139r.com|bet164.com|yinlijun|905087797|www.niu21.com|www.26566.com|www.q9966.com|www.hg2926.com|www. 391be. com|wwwxmsycom|xpj9151com|yummm|www.44998.com|piziai22dj|www.jmhdj.com|bet6096.com|msc993.com|16219com|js7626|www.474l88.com|www.xmav18.com|9622.com|www33398com|www.k9lll.com|20577.com|wwwmg8166com|www.585sun.com|bdjiasuqi.com|9486-c|wwwjs638co|sophy312|www.90855.com|www.tianshi.com|c11277|1630bet|蓝天航空|jj0123|m.jyhuwyxi8v.cn|99qiezipw|agks81.com|www.005|lang585.com|www.ruient.com|zjy11441144|eee223|yabet3524com|www.qlshwlq.com|www.pitetv. con|wuwu55|cvc9999|ks6527.vip|yabo5301com|wwwhg15123com|www.jsdc952.com|www.th68.me|www.q1268.com|87680y|25c25xxx|8845.com|www avtt3 co|wwwamjs9990com|www941vnscom|www.c468888.com|caige|7664819|88833-9.com|WWW. yyv. co|hl8088com|www.88444.hk|257kk新域名|11744.com|www.6885n.com|www.d15999.cn|www013875com|55310pp.com|www.84688.com|www.kz6688.com|www.489411.com|www88tbcom|ti.qqcom|www.ppk222.com|rr36590.com|wwwWANDA04COM|www22355cnm|www.138778.com|www.155921.com|dhy2288.com|www.9343.com|v9337.com|www.hk36188.com|55epep最新地址|soso|https://wwwhs943com/|

www.33zb. com|www.484111.com|www.lloyds.com.cn|ag6529com|jidu46|gjk666|q2naav20|www.bly222.com|kongtao668|mjs08.com|vns3803com|08087.com|liuhecai163com|www.kk1xx.com|wwwxpj8717899com|e83377.com|www77605dcom|www1095com|www.44678.cc|yb9480com|25338.com|lushuang|2824fcom|WWW.WWW.JS666685.COM|901ccccnm永久观看地址901|ys4499com|www.ks337.net|www.wyl360.com|ag.61022.com|5626bet|hs444.cn|892059com|c791836718|zzsve.com|blm2233com|www.560104.com|10050372|whl123|WWW.TM018.COM|www.dgbyg.con|47cai.com|lock|www777888com|www.49956.com|wwwam8778com|901ccccnm永久观看地址|www58148com|sihu2019最新地址是什么啊|99184.com|www.66098811.com|www3478com|4466k|www.88BET05.COM|liuhe58.com|qp9953.com|60820.vip”|www.22911.com|jyd8899.com|vns4568com|52ppyycom网站免费观看|mtianxiahuizhoucom|czjg8880|www.1231777.com|www.pj666666.com|91视频 www.gxbol.com|GJWX86/IYL|mhc006com|www.2016mq.com|www.007casinoroyale.com|6677.hk|5031.com|reya|6590e.com|c557888|wwwbet5849com|m6777.com|980xycom|www.47es.com|qizhe08|WWW.26965.COM|wwwhaoli797com|www.biquge.com|www.888711.com|tgtf|WWW.HG3577.COM|839274com|www.513jr.com|ww130222com|www.99ra7.com|585ccc.com|www.236688.com|qwe3ty|876777.com|wwwccpnet|7935m.net|www.3a98.com|smluntan|www.485250.com|www.5858.cc|55455a. com|www. 58pao. com|657000.com|70888bb.com|liu3340|www.0533.com|wwwule8vip|gang0011|www.577.com|30177777|www.sdcp.cn|tfa24|WWW.D38.CC|1750m.com|ag7119vip|a15551|fxm369|www.4866.com|411ss1sss1111211crt4wf7cn/?p=490'|a454649221|aaa12111|kb1003com|WWW.GX.NET|wwwks6697com|www440858com|www.888mimi.com|yan61|wwwlive7m66com|www 0284hu com|xiedehua|6834ww.com|www.pjxinjiang.com|www.pj9590.com|wwwhg4128com|ylzz977.com|www.hy946.com|787ccccom|cc65195690|w8w8w8w88|940828|www.6698Z|www.3313cc.com|youle88.cc|23111jscom|hbxkwycom|www.tcsy.com|www.aa658.com|jtlzjjcom|WWW.7004.AM|0866bet|www.222238.com|WWW.55GF.COM|www.hg516.com|www9555kcom|www9994403com|m958|871mk.com|ZC518.NET|k55111.com|hp559.com|www.se97.com|www.vip218.com|www.667ha.com|chaile1118|111999js.com|www.avtt5547.com|wwwxpj1372com|18499.com|wwwwanyi777com|

以上会员名单排名不分前后