三角函數(shù)講義6

1、專業(yè)好文檔第6講 函數(shù)y=asin(x+)的圖象及三角函數(shù)模型的簡(jiǎn)單應(yīng)用1、考綱點(diǎn)擊（1）了解函數(shù)y=asin(x+)的物理意義；能畫(huà)出函數(shù)y=asin(x+)的圖象，了解參數(shù)a，對(duì)函數(shù)圖象變化的影響；（2）了解三角函數(shù)是描述周期變化現(xiàn)象的重要函數(shù)模型，會(huì)用三角函數(shù)解決一些簡(jiǎn)單實(shí)際問(wèn)題。2、熱點(diǎn)提示（1）用“五點(diǎn)作圖法”作函數(shù)y=asin(x+)的圖象；（2）圖象的變換規(guī)律：平移和伸縮變換在主、客觀題中均考查；（3）結(jié)合三角恒等變換考查y=asin(x+)性質(zhì)及簡(jiǎn)單應(yīng)用是考查的熱點(diǎn)。知識(shí)整合：簡(jiǎn)諧運(yùn)動(dòng)的有關(guān)概念簡(jiǎn)諧運(yùn)動(dòng)圖象的解析式振幅周期頻率相位初相y=asin(x+)（a0, 0）x0.+）

2、at=x+2、用五點(diǎn)法畫(huà)y=asin(x+)一個(gè)周期內(nèi)的簡(jiǎn)圖用五點(diǎn)法畫(huà)y=asin(x+)一個(gè)周期內(nèi)的簡(jiǎn)圖時(shí)，要找五個(gè)關(guān)鍵點(diǎn)，如表所示x+02xy=asin(x+)0a0-a0注：在上表的三行中，找五個(gè)點(diǎn)時(shí)，首先確定第一行的數(shù)據(jù)，即先使x+=0，2然后求出x的值。3、函數(shù)y=sinx的圖象經(jīng)變換得到y(tǒng)=asin(x+)的圖象的步驟典例分析：1、函數(shù)的圖象例1 已知函數(shù)。（1）作出函數(shù)在區(qū)間上的圖象（2）求函數(shù)在區(qū)間上的最大值和最小值。思路解析：（1）把化簡(jiǎn)為的形式，然后列表，畫(huà)圖象；（2）先求出x+在上的范圍，然后根據(jù)單調(diào)性求解。解答：（1）=cos2x-sin2x=cos(2x+).列表：2

3、x+2x01001圖象如圖：（2）,當(dāng)，即x= 時(shí)，有最小值，min=-1,當(dāng)2x+ =0，即x= 時(shí)，有最大值，max=,即在，0上的最小值為-1，最大值為。2、函數(shù)+b的解析式例2函數(shù)f(x)asin(x) 的部分圖象如圖所示(1)求f(x)的解析式；(2)設(shè)g(x)2，求函數(shù)g(x)在x上的最大值，并確定此時(shí)x的值解：(1)由圖知a2，則4，.又f2sin2sin0，sin0，0，0，即，f(x)的解析式為f(x)2sin.(2)由(1)可得f2sin2sin，g(x)24422cos，x，3x，當(dāng)3x，即x時(shí)，g(x)max4. 3、函數(shù)y=asin(x+)的圖象與性質(zhì)的綜合應(yīng)用例3已

4、知函數(shù)f(x)12sinxcosx2cos2x.(1)求f(x)的單調(diào)遞減區(qū)間；(2)求f(x)圖象上與原點(diǎn)最近的對(duì)稱中心的坐標(biāo)；(3)若角，的終邊不共線，且f()f()，求tan()的值解析 f(x)sin2xcos2x2sin(2x)，(1)由2k2x2k(kz)得kxk(kz)，f(x)的單調(diào)減區(qū)間為k，k(kz)，(2)由sin(2x)0得2xk(kz)，即x(kz)，f(x)圖象上與原點(diǎn)最近的對(duì)稱中心坐標(biāo)是(，0)(3)由f()f()得：2sin(2)2sin(2)，又角與的終邊不共線，(2)(2)2k(kz)，即k(kz)，tan(). 4、函數(shù)y=asin(x+)+b模型的簡(jiǎn)單應(yīng)

5、用例4以一年為一個(gè)周期調(diào)查某商品出廠價(jià)格及該商品在商店的銷售價(jià)格時(shí)發(fā)現(xiàn)：該商品的出廠價(jià)格是在6元基礎(chǔ)上按月份隨正弦曲線波動(dòng)的，已知3月份出廠價(jià)格最高為8元，7月份出廠價(jià)格最低為4元，而該商品在商店的銷售價(jià)格是在8元基礎(chǔ)上按月隨正弦曲線波動(dòng)的，并已知5月份銷售價(jià)最高為10元，9月份銷售價(jià)最低為6元，假設(shè)某商店每月購(gòu)進(jìn)這種商品m件，且當(dāng)月售完，請(qǐng)估計(jì)哪個(gè)月盈利最大？并說(shuō)明理由.解：由條件可得：出廠價(jià)格函數(shù)為, 銷售價(jià)格函數(shù)為則利潤(rùn)函數(shù)為: 所以，當(dāng)時(shí)，y=（2+）m，即6月份盈利最大.winger tuivasa-sheck, who scored two tries in the kiwis 2

6、0-18 semi-final win over england, has been passed fit after a lower-leg injury, while slater has been named at full-back but is still recovering from a knee injury aggravated against usa.both sides boast 100% records heading into the encounter but australia have not conceded a try since josh charnle

7、ys effort in their first pool match against england on the opening day.aussie winger jarryd hayne is the competitions top try scorer with nine, closely followed by tuivasa-sheck with eight.but it is recently named rugby league international federation player of the year sonny bill williams who has a

8、ttracted the most interest in the tournament so far.the kiwi - with a tournament high 17 offloads - has the chance of becoming the first player to win the world cup in both rugby league and rugby union after triumphing with the all blacks in 2011.id give every award back in a heartbeat just to get a

9、cross the line this weekend, said williams.the (lack of) air up there watch mcayman islands-based webb, the head of fifas anti-racism taskforce, is in london for the football associations 150th anniversary celebrations and will attend citys premier league match at chelsea on sunday.i am going to be

10、at the match tomorrow and i have asked to meet yaya toure, he told bbc sport.for me its about how he felt and i would like to speak to him first to find out what his experience was.uefa hasopened disciplinary proceedings against cskafor the racist behaviour of their fans duringcitys 2-1 win.michel p

11、latini, president of european footballs governing body, has also ordered an immediate investigation into the referees actions.cska said they were surprised and disappointed by toures complaint. in a statement the russian side added: we found no racist insults from fans of cska. baumgartner the disap

12、pointing news: mission aborted.the supersonic descent could happen as early as sunda.the weather plays an important role in this mission. starting at the ground, conditions have to be very calm - winds less than 2 mph, with no precipitation or humidity and limited cloud cover. the balloon, with caps

13、ule attached, will move through the lower level of the atmosphere (the troposphere) where our day-to-day weather lives. it will climb higher than the tip of mount everest (5.5 miles/8.85 kilometers), drifting even higher than the cruising altitude of commercial airliners (5.6 miles/9.17 kilometers)

14、and into the stratosphere. as he crosses the boundary layer (called the tropopause),e can expect a lot of turbulence.the balloon will slowly drift to the edge of space at 120,000 feet ( then, i would assume, he will slowly step out onto something resembling an olympic diving platform.they blew it in

15、 2008 when they got caught cold in the final and they will not make the same mistake against the kiwis in manchester.five years ago they cruised through to the final and so far history has repeated itself here - the last try they conceded was scored by englands josh charnley in the opening game of t

16、he tournament.that could be classed as a weakness, a team under-cooked - but i have been impressed by the kangaroos focus in their games since then.they have been concentrating on the sort of stuff that wins you tough, even contests - strong defence, especially on their own goal-line, completing set

17、s and a good kick-chase. theyve been great at all the unglamorous stuff that often goes unnoticed in the stands but not by your team-mates.it is as though their entire tournament has been preparation for the final.in johnathan thurston, cooper cronk, cameron smith and either billy slater or greg inglis at full-back they have a spine that is unmatched in rugby league. they have played in so many high-pressure games - a priceless asset going into