三角函数讲义6

1、专业好文档第6讲 函数y=asin(x+)的图象及三角函数模型的简单应用1、考纲点击（1）了解函数y=asin(x+)的物理意义；能画出函数y=asin(x+)的图象，了解参数a，对函数图象变化的影响；（2）了解三角函数是描述周期变化现象的重要函数模型，会用三角函数解决一些简单实际问题。2、热点提示（1）用“五点作图法”作函数y=asin(x+)的图象；（2）图象的变换规律：平移和伸缩变换在主、客观题中均考查；（3）结合三角恒等变换考查y=asin(x+)性质及简单应用是考查的热点。知识整合：简谐运动的有关概念简谐运动图象的解析式振幅周期频率相位初相y=asin(x+)（a0, 0）x0.+）

2、at=x+2、用五点法画y=asin(x+)一个周期内的简图用五点法画y=asin(x+)一个周期内的简图时，要找五个关键点，如表所示x+02xy=asin(x+)0a0-a0注：在上表的三行中，找五个点时，首先确定第一行的数据，即先使x+=0，2然后求出x的值。3、函数y=sinx的图象经变换得到y=asin(x+)的图象的步骤典例分析：1、函数的图象例1 已知函数。（1）作出函数在区间上的图象（2）求函数在区间上的最大值和最小值。思路解析：（1）把化简为的形式，然后列表，画图象；（2）先求出x+在上的范围，然后根据单调性求解。解答：（1）=cos2x-sin2x=cos(2x+).列表：2

3、x+2x01001图象如图：（2）,当，即x= 时，有最小值，min=-1,当2x+ =0，即x= 时，有最大值，max=,即在，0上的最小值为-1，最大值为。2、函数+b的解析式例2函数f(x)asin(x) 的部分图象如图所示(1)求f(x)的解析式；(2)设g(x)2，求函数g(x)在x上的最大值，并确定此时x的值解：(1)由图知a2，则4，.又f2sin2sin0，sin0，0，0，即，f(x)的解析式为f(x)2sin.(2)由(1)可得f2sin2sin，g(x)24422cos，x，3x，当3x，即x时，g(x)max4. 3、函数y=asin(x+)的图象与性质的综合应用例3已

4、知函数f(x)12sinxcosx2cos2x.(1)求f(x)的单调递减区间；(2)求f(x)图象上与原点最近的对称中心的坐标；(3)若角，的终边不共线，且f()f()，求tan()的值解析 f(x)sin2xcos2x2sin(2x)，(1)由2k2x2k(kz)得kxk(kz)，f(x)的单调减区间为k，k(kz)，(2)由sin(2x)0得2xk(kz)，即x(kz)，f(x)图象上与原点最近的对称中心坐标是(，0)(3)由f()f()得：2sin(2)2sin(2)，又角与的终边不共线，(2)(2)2k(kz)，即k(kz)，tan(). 4、函数y=asin(x+)+b模型的简单应

5、用例4以一年为一个周期调查某商品出厂价格及该商品在商店的销售价格时发现：该商品的出厂价格是在6元基础上按月份随正弦曲线波动的，已知3月份出厂价格最高为8元，7月份出厂价格最低为4元，而该商品在商店的销售价格是在8元基础上按月随正弦曲线波动的，并已知5月份销售价最高为10元，9月份销售价最低为6元，假设某商店每月购进这种商品m件，且当月售完，请估计哪个月盈利最大？并说明理由.解：由条件可得：出厂价格函数为, 销售价格函数为则利润函数为: 所以，当时，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