三角函数讲义3

1、专业好文档第3讲 两角和与差的正弦、余弦和正切公式1、考纲点击（1）会用向量的数量积推导出两角差的余弦公式；（2）能利用两角差的余弦公式导出两角差的正弦、正切公式；（3）能利用两角差的余弦公式导出两角和的正弦、余弦、正切公式，导出二倍角的正弦、余弦、正切公式，了解它们的内在联系。2、热点提示（1）利用两角和与差的正弦、余弦、正切公式进行三角函数式的化简求值是高考常考点；（3）对asinx+bcosx的化简是高考每年必考内容；（4）在选择、填空、解答题中都可以考查。知识整合：1、两角和与差的正弦、余弦和正切公式2、二倍角的正弦、余弦、正切公式.3、形如asin+bcos的化简.其中cos= ,s

2、in= 典例分析：1、三角函数式的化简、求值例1化简：（1）；（2）（1）分析一：降次，切化弦解法一：原式=分析二：变“复角”为“单角”解法二：原式（2）原式=，原式=点评：化简本质就是化繁为简，一般从结构，名称，角等几个角度入手如：切化弦，“复角”变“单角”，降次等2、 三角函数的给角求值问题例2.求值：（1）；（2）分析：切化弦，通分解：（1）原式=（2），又原式=点评：给角求值，注意寻找所给角与特殊角的联系，如互余，互补等，利用诱导公式，和与差公式，二倍角公式进行转换3、 三角函数的给值求值问题例3设，且，求，分析：， 解：由，得，同理，可得，同理，得点评：寻求“已知角”与“未知角”之间

3、的联系，如：，等例4若，求的值分析一：解法一：，又，所以，原式=分析二：解法二：原式=又，所以，原式点评：观察“角”之间的联系以寻找解题思路4、三角函数的给值求角问题例4(2011珠海模拟)已知a、b均为钝角且sina，sinb，求ab的值解析 a、b均为钝角且sina，sinb，cosa，cosb，cos(ab)cosacosbsinasinb()，又a，b，ab2，ab.5.三角函数在三角形中的应用例5 在中，求和的值。解：由，且故 由，且则 或由于，故，即为锐角。 又由 winger tuivasa-sheck, who scored two tries in the kiwis 20-

4、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 charnleys

5、 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 att

6、racted 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 acr

7、oss 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 at

8、 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 pla

9、tini, 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 disappo

10、inting 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 capsul

11、e 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) an

12、d 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 2

13、008 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 the

14、 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 sets

15、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 saturday.the kiwis are a lot