三角函數(shù)講義5.doc

1、專業(yè)好文檔第5講 三角函數(shù)的圖象與性質(zhì)1、考綱點(diǎn)擊（1）能畫出y=sinx, y=cosx, y=tanx的圖象，了解三角函數(shù)的周期性；（2）理解正弦函數(shù)、余弦函數(shù)在區(qū)間0，2上的性質(zhì)（如單調(diào)性、最大值和最小值以及與x軸的交點(diǎn)等），理解正切函數(shù)在區(qū)間內(nèi)的單調(diào)性。2、熱點(diǎn)提示（1）三角函數(shù)的值域、最值、單調(diào)性、周期性等性質(zhì)是高考考查的重點(diǎn)；（2）三角函數(shù)的對(duì)稱性也是高考的一個(gè)熱點(diǎn)；（3）主要以選擇題、填空題的形式考查。知識(shí)整合：1、周期函數(shù)（1）周期函數(shù)的定義對(duì)于函數(shù)f(x)，如果存在一個(gè)非零常數(shù)T，使得當(dāng)x取定義域內(nèi)的每一個(gè)值時(shí)，都有f(x+T)=f(x),那么函數(shù)f(x)就叫做周期函數(shù)。非零

2、常數(shù)T叫做這個(gè)函數(shù)的周期。（2）最小正周期如果在周期函數(shù)f(x)的所有周期中存在一個(gè)最小的正數(shù)，那么這個(gè)最小正數(shù)就叫做f(x)的最小正周期。注：如果函數(shù)y=f(x)的周期是T，則函數(shù)y=f(x)周期是，而不是。2、正弦函數(shù)、余弦函數(shù)、正切函數(shù)的圖象和性質(zhì)函數(shù)y=sinxy=cosxy=tanx圖象定義域xRxRxR且值域y|-1y1y|-1y1R單調(diào)性最值無(wú)最值奇偶性奇偶奇對(duì)稱性對(duì)稱中心（k,0）,kZ（k+,0）,kZ（,0）,kZ對(duì)稱軸x= k+,kZx= k,kZ無(wú)周期22注：y=sinx與y=cosx的對(duì)稱軸方程中的x都是它們?nèi)〉米畲笾祷蜃钚≈禃r(shí)相應(yīng)的x，對(duì)稱中心的橫坐標(biāo)都是它們的零點(diǎn)

3、。典例分析：1、與三角函數(shù)有關(guān)的函數(shù)的定義域例1例1.求下列函數(shù)的定義域：（1）；（2）解：（1）即，故函數(shù)的定義域?yàn)榍遥?）即故函數(shù)的定義域?yàn)辄c(diǎn)評(píng)：由幾個(gè)函數(shù)的和構(gòu)成的函數(shù)，其定義域是每一個(gè)函數(shù)定義域的交集；第（2）問(wèn)可用數(shù)軸取交集2、三角函數(shù)單調(diào)區(qū)間的求法例2求下列函數(shù)的單調(diào)減區(qū)間：（1）； （2）；解：（1）因?yàn)椋试瘮?shù)的單調(diào)減區(qū)間為（2）由，得，又，所以該函數(shù)遞減區(qū)間為，即點(diǎn)評(píng)：利用復(fù)合函數(shù)求單調(diào)區(qū)間應(yīng)注意定義域的限制3、三角函數(shù)的最小正周期例3求下列函數(shù)的最小正周期：（1）；（2） 解：（1）由函數(shù)的最小正周期為，得的周期（2） 4、三角函數(shù)的值域與最值例4（1）已知，求的最大值與

4、最小值（2）求函數(shù)的最大值（3）求函數(shù)的最小值解：（1）由已知得：，則，當(dāng)時(shí)，有最小值；當(dāng)時(shí)，有最小值（2）設(shè)，則，則，當(dāng)時(shí)，有最大值為（3）解法一：原式可化為，得，即，故，解得或（舍），所以的最小值為解法二：表示的是點(diǎn)與連線的斜率，其中點(diǎn)B在左半圓上，由圖像知，當(dāng)AB與半圓相切時(shí)，最小，此時(shí)，所以的最小值為點(diǎn)評(píng)：第（1）小題利用消元法，第（2）小題利用換元法最終都轉(zhuǎn)化為二次函數(shù)求最值問(wèn)題；但要注意變量的取值范圍（3）解法一利用三角函數(shù)的有界性求解；解法二從結(jié)構(gòu)出發(fā)利用斜率公式，結(jié)合圖像求解例5.已知函數(shù)，（I）求的最大值和最小值； （II）若不等式在上恒成立，求實(shí)數(shù)的取值范圍分析：觀察角，單

5、角二次型，降次整理為形式 解：（） 又，即，（），且，即的取值范圍是Winger Tuivasa-Sheck, who scored two tries in the Kiwis' 20-18 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

6、100% records heading into the encounter but Australia have not conceded a try since Josh Charnley's effort in their first pool match against England on the opening day.Aussie winger Jarryd Hayne is the competition's top try scorer with nine, closely followed by Tuivasa-Sheck with eight.But i

7、t is recently named Rugby League International Federation player of the year Sonny Bill Williams who has attracted 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 rugb

8、y union after triumphing with the All Blacks in 2011."I'd give every award back in a heartbeat just to get across the line this weekend," said Williams.The (lack of) air up there Watch mCayman Islands-based Webb, the head of Fifa's anti-racism taskforce, is in London for the Footba

9、ll Association's 150th anniversary celebrations and will attend City's Premier League match at Chelsea on Sunday."I am going to be at the match tomorrow and I have asked to meet Yaya Toure," he told BBC Sport."For me it's about how he felt and I would like to speak to him

10、first to find out what his experience was."Uefa has opened disciplinary proceedings against CSKA for the "racist behaviour of their fans" during City's 2-1 win.Michel Platini, president of European football's governing body, has also ordered an immediate investi

11、gation into the referee's actions.CSKA said they were "surprised and disappointed" by Toure's complaint. In a statement the Russian side added: "We found no racist insults from fans of CSKA." Baumgartner the disappointing news: Mission aborted.The supersonic descent could

12、 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 capsule attached, will move through the lower level of the atmo

13、sphere (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) and into the stratosphere. As he crosses the boundary layer

14、 (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 2008 when they got caught cold in the final and they will

15、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 England's Josh Charnley in the opening game of the tournament.That could be classed as a weakness, a t

16、eam 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 sets and a good kick-chase. They've been great a

17、t 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 S