2022年人教A版数学必修四1.4.2《正弦、余弦函数的性质》Word教案1 .pdf

名师精编优秀教案1.4.2 正弦、余弦函数的性质教学目标：1、知识与技能掌握正弦函数和余弦函数的性质2、过程与能力目标通过引导学生观察正、余弦函数的图像，从而发现正、余弦函数的性质，加深对性质的理解并会求简单函数的定义域、值域、最小正周期和单调区间3、情感与态度目标渗透数形结合思想，培养学生辩证唯物主义观点教学重点：正、余弦函数的周期性；正、余弦函数的奇、偶性和单调性。教学难点：正、余弦函数周期性的理解与应用；正、余弦函数奇、偶性和单调性的理解与应用。正弦、余弦函数的性质(一)教学过程：一、复习引入：1问题：（1）今天是星期一，则过了七天是星期几？过了十四天呢？（2）物理中的单摆振动、圆周运动，质点运动的规律如何呢？2观察正（余）弦函数的图象总结规律：自变量x232202322函数值sinx0010010正弦函数()sinfxx性质如下：（观察图象）1正弦函数的图象是有规律不断重复出现的；2规律是：每隔2 重复出现一次（或者说每隔2k,kZ 重复出现）3这个规律由诱导公式sin(2k+x)=sinx可以说明结论：象这样一种函数叫做周期函数。文字语言：正弦函数值按照一定的规律不断重复地取得；符号语言：当x增加2k（kZ）时，总有(2)sin(2)sin()f xkxkxf x也即：（1）当自变量x增加2k时，正弦函数的值又重复出现；（2）对于定义域内的任意x，sin(2)sinxkx恒成立。222525Oxy11名师精编优秀教案余弦函数也具有同样的性质，这种性质我们就称之为周期性。二、讲解新课：1周期函数定义：对于函数f(x)，如果存在一个非零常数T，使得当x 取定义域内的每一个值时，都有：f(x+T)=f(x)那么函数f(x)就叫做周期函数，非零常数T 叫做这个函数的周期。问题：（1）对于函数sinyx，xR有2sin()sin636，能否说23是它的周期？（2）正弦函数sinyx，xR是不是周期函数，如果是，周期是多少？（2k，kZ且0k）（3）若函数()f x的周期为T，则kT，*kZ也是()f x的周期吗？为什么？（是，其原因为：()()(2)()f xf xTf xTfxkT）2、说明：1 周期函数 x定义域 M，则必有x+T M,且若 T0 则定义域无上界；T0 则定义域无下界；2“每一个值”只要有一个反例，则f(x)就不为周期函数（如f(x0+t)f(x0)）3T 往往是多值的（如y=sinx 2,4,-2,-4,都是周期）周期T 中最小的正数叫做f(x)的最小正周期（有些周期函数没有最小正周期）y=sinx,y=cosx的最小正周期为2（一般称为周期）从图象上可以看出sinyx，xR；cosyx，xR的最小正周期为2；判断：是不是所有的周期函数都有最小正周期？（()f xc没有最小正周期）3、例题讲解例 1 求下列三角函数的周期：xycos3xy2sin（3）12sin()26yx，xR解：（1）3cos(2)3cosxx，自变量x只要并且至少要增加到2x，函数3cosyx，xR的值才能重复出现，所以，函数3cosyx，xR的周期是2（2）sin(22)sin 2()sin2xxx，自变量x只要并且至少要增加到x，函数sin 2yx，xR的值才能重复出现，所以，函数sin2yx，xR的周期是文档编码:CN5F1C2Z4K9 HW10A1N2H10V10 ZD2D10D6J9Z7文档编码:CN5F1C2Z4K9 HW10A1N2H10V10 ZD2D10D6J9Z7文档编码:CN5F1C2Z4K9 HW10A1N2H10V10 ZD2D10D6J9Z7文档编码:CN5F1C2Z4K9 HW10A1N2H10V10 ZD2D10D6J9Z7文档编码:CN5F1C2Z4K9 HW10A1N2H10V10 ZD2D10D6J9Z7文档编码:CN5F1C2Z4K9 HW10A1N2H10V10 ZD2D10D6J9Z7文档编码:CN5F1C2Z4K9 HW10A1N2H10V10 ZD2D10D6J9Z7文档编码:CN5F1C2Z4K9 HW10A1N2H10V10 ZD2D10D6J9Z7文档编码:CN5F1C2Z4K9 HW10A1N2H10V10 ZD2D10D6J9Z7文档编码:CN5F1C2Z4K9 HW10A1N2H10V10 ZD2D10D6J9Z7文档编码:CN5F1C2Z4K9 HW10A1N2H10V10 ZD2D10D6J9Z7文档编码:CN5F1C2Z4K9 HW10A1N2H10V10 ZD2D10D6J9Z7文档编码:CN5F1C2Z4K9 HW10A1N2H10V10 ZD2D10D6J9Z7文档编码:CN5F1C2Z4K9 HW10A1N2H10V10 ZD2D10D6J9Z7文档编码:CN5F1C2Z4K9 HW10A1N2H10V10 ZD2D10D6J9Z7文档编码:CN5F1C2Z4K9 HW10A1N2H10V10 ZD2D10D6J9Z7文档编码:CN5F1C2Z4K9 HW10A1N2H10V10 ZD2D10D6J9Z7文档编码:CN5F1C2Z4K9 HW10A1N2H10V10 ZD2D10D6J9Z7文档编码:CN5F1C2Z4K9 HW10A1N2H10V10 ZD2D10D6J9Z7文档编码:CN5F1C2Z4K9 HW10A1N2H10V10 ZD2D10D6J9Z7文档编码:CN5F1C2Z4K9 HW10A1N2H10V10 ZD2D10D6J9Z7文档编码:CN5F1C2Z4K9 HW10A1N2H10V10 ZD2D10D6J9Z7文档编码:CN5F1C2Z4K9 HW10A1N2H10V10 ZD2D10D6J9Z7文档编码:CN5F1C2Z4K9 HW10A1N2H10V10 ZD2D10D6J9Z7文档编码:CN5F1C2Z4K9 HW10A1N2H10V10 ZD2D10D6J9Z7文档编码:CN5F1C2Z4K9 HW10A1N2H10V10 ZD2D10D6J9Z7文档编码:CN5F1C2Z4K9 HW10A1N2H10V10 ZD2D10D6J9Z7文档编码:CN5F1C2Z4K9 HW10A1N2H10V10 ZD2D10D6J9Z7文档编码:CN5F1C2Z4K9 HW10A1N2H10V10 ZD2D10D6J9Z7文档编码:CN5F1C2Z4K9 HW10A1N2H10V10 ZD2D10D6J9Z7文档编码:CN5F1C2Z4K9 HW10A1N2H10V10 ZD2D10D6J9Z7文档编码:CN5F1C2Z4K9 HW10A1N2H10V10 ZD2D10D6J9Z7文档编码:CN5F1C2Z4K9 HW10A1N2H10V10 ZD2D10D6J9Z7文档编码:CN5F1C2Z4K9 HW10A1N2H10V10 ZD2D10D6J9Z7文档编码:CN5F1C2Z4K9 HW10A1N2H10V10 ZD2D10D6J9Z7文档编码:CN5F1C2Z4K9 HW10A1N2H10V10 ZD2D10D6J9Z7文档编码:CN5F1C2Z4K9 HW10A1N2H10V10 ZD2D10D6J9Z7文档编码:CN5F1C2Z4K9 HW10A1N2H10V10 ZD2D10D6J9Z7文档编码:CN5F1C2Z4K9 HW10A1N2H10V10 ZD2D10D6J9Z7文档编码:CN5F1C2Z4K9 HW10A1N2H10V10 ZD2D10D6J9Z7文档编码:CN5F1C2Z4K9 HW10A1N2H10V10 ZD2D10D6J9Z7文档编码:CN5F1C2Z4K9 HW10A1N2H10V10 ZD2D10D6J9Z7文档编码:CN5F1C2Z4K9 HW10A1N2H10V10 ZD2D10D6J9Z7文档编码:CN5F1C2Z4K9 HW10A1N2H10V10 ZD2D10D6J9Z7文档编码:CN5F1C2Z4K9 HW10A1N2H10V10 ZD2D10D6J9Z7文档编码:CN5F1C2Z4K9 HW10A1N2H10V10 ZD2D10D6J9Z7文档编码:CN5F1C2Z4K9 HW10A1N2H10V10 ZD2D10D6J9Z7文档编码:CN5F1C2Z4K9 HW10A1N2H10V10 ZD2D10D6J9Z7名师精编优秀教案（3）1112sin(2)2sin()2sin()262626xxx，自变量x只要并且至少要增加到x，函数sin2yx，xR的值才能重复出现，所以，函数sin 2yx，xR的周期是练习 1。求下列三角函数的周期：1 y=sin(x+3)2 y=cos2x 3 y=3sin(2x+5)解：1令 z=x+3而 sin(2+z)=sinz 即：f(2+z)=f(z)f(x+2)+3=f(x+3)周期 T=22 令 z=2x f(x)=cos2x=cosz=cos(z+2)=cos(2x+2)=cos2(x+)即：f(x+)=f(x)T=3令 z=2x+5则：f(x)=3sinz=3sin(z+2)=3sin(2x+5+2)=3sin(524x)=f(x+4)T=4思考：从上例的解答过程中归纳一下这些函数的周期与解析式中的哪些量有关？说明：（1）一般结论：函数sin()yAx及函数cos()yAx，xR（其中,A为常数，且0A，0）的周期2T；（2）若0，如：3cos()yx；sin(2)yx；12sin()26yx，xR则这三个函数的周期又是什么？一般结论：函数sin()yAx及函数cos()yAx，xR的周期2|T思考：求下列函数的周期：1 y=sin(2x+4)+2cos(3x-6)2 y=|sinx|解：1 y1=sin(2x+4)最小正周期T1=y2=2cos(3x-6)最小正周期 T2=32T 为 T1,T2的最小公倍数2T=2 2 T=作图三、巩固与练习P36 面四、小结：本节课学习了以下内容：周期函数的定义，周期，最小正周期五、课后作业：23-文档编码:CL9Y3C6P9F4 HH2C3D3N1V1 ZM9M2Z3B7P10文档编码:CL9Y3C6P9F4 HH2C3D3N1V1 ZM9M2Z3B7P10文档编码:CL9Y3C6P9F4 HH2C3D3N1V1 ZM9M2Z3B7P10文档编码:CL9Y3C6P9F4 HH2C3D3N1V1 ZM9M2Z3B7P10文档编码:CL9Y3C6P9F4 HH2C3D3N1V1 ZM9M2Z3B7P10文档编码:CL9Y3C6P9F4 HH2C3D3N1V1 ZM9M2Z3B7P10文档编码:CL9Y3C6P9F4 HH2C3D3N1V1 ZM9M2Z3B7P10文档编码:CL9Y3C6P9F4 HH2C3D3N1V1 ZM9M2Z3B7P10文档编码:CL9Y3C6P9F4 HH2C3D3N1V1 ZM9M2Z3B7P10文档编码:CL9Y3C6P9F4 HH2C3D3N1V1 ZM9M2Z3B7P10文档编码:CL9Y3C6P9F4 HH2C3D3N1V1 ZM9M2Z3B7P10文档编码:CL9Y3C6P9F4 HH2C3D3N1V1 ZM9M2Z3B7P10文档编码:CL9Y3C6P9F4 HH2C3D3N1V1 ZM9M2Z3B7P10文档编码:CL9Y3C6P9F4 HH2C3D3N1V1 ZM9M2Z3B7P10文档编码:CL9Y3C6P9F4 HH2C3D3N1V1 ZM9M2Z3B7P10文档编码:CL9Y3C6P9F4 HH2C3D3N1V1 ZM9M2Z3B7P10文档编码:CL9Y3C6P9F4 HH2C3D3N1V1 ZM9M2Z3B7P10文档编码:CL9Y3C6P9F4 HH2C3D3N1V1 ZM9M2Z3B7P10文档编码:CL9Y3C6P9F4 HH2C3D3N1V1 ZM9M2Z3B7P10文档编码:CL9Y3C6P9F4 HH2C3D3N1V1 ZM9M2Z3B7P10文档编码:CL9Y3C6P9F4 HH2C3D3N1V1 ZM9M2Z3B7P10文档编码:CL9Y3C6P9F4 HH2C3D3N1V1 ZM9M2Z3B7P10文档编码:CL9Y3C6P9F4 HH2C3D3N1V1 ZM9M2Z3B7P10文档编码:CL9Y3C6P9F4 HH2C3D3N1V1 ZM9M2Z3B7P10文档编码:CL9Y3C6P9F4 HH2C3D3N1V1 ZM9M2Z3B7P10文档编码:CL9Y3C6P9F4 HH2C3D3N1V1 ZM9M2Z3B7P10文档编码:CL9Y3C6P9F4 HH2C3D3N1V1 ZM9M2Z3B7P10文档编码:CL9Y3C6P9F4 HH2C3D3N1V1 ZM9M2Z3B7P10文档编码:CL9Y3C6P9F4 HH2C3D3N1V1 ZM9M2Z3B7P10文档编码:CL9Y3C6P9F4 HH2C3D3N1V1 ZM9M2Z3B7P10文档编码:CL9Y3C6P9F4 HH2C3D3N1V1 ZM9M2Z3B7P10文档编码:CL9Y3C6P9F4 HH2C3D3N1V1 ZM9M2Z3B7P10文档编码:CL9Y3C6P9F4 HH2C3D3N1V1 ZM9M2Z3B7P10文档编码:CL9Y3C6P9F4 HH2C3D3N1V1 ZM9M2Z3B7P10文档编码:CL9Y3C6P9F4 HH2C3D3N1V1 ZM9M2Z3B7P10文档编码:CL9Y3C6P9F4 HH2C3D3N1V1 ZM9M2Z3B7P10文档编码:CL9Y3C6P9F4 HH2C3D3N1V1 ZM9M2Z3B7P10文档编码:CL9Y3C6P9F4 HH2C3D3N1V1 ZM9M2Z3B7P10文档编码:CL9Y3C6P9F4 HH2C3D3N1V1 ZM9M2Z3B7P10文档编码:CL9Y3C6P9F4 HH2C3D3N1V1 ZM9M2Z3B7P10文档编码:CL9Y3C6P9F4 HH2C3D3N1V1 ZM9M2Z3B7P10文档编码:CL9Y3C6P9F4 HH2C3D3N1V1 ZM9M2Z3B7P10文档编码:CL9Y3C6P9F4 HH2C3D3N1V1 ZM9M2Z3B7P10文档编码:CL9Y3C6P9F4 HH2C3D3N1V1 ZM9M2Z3B7P10文档编码:CL9Y3C6P9F4 HH2C3D3N1V1 ZM9M2Z3B7P10文档编码:CL9Y3C6P9F4 HH2C3D3N1V1 ZM9M2Z3B7P10文档编码:CL9Y3C6P9F4 HH2C3D3N1V1 ZM9M2Z3B7P10文档编码:CL9Y3C6P9F4 HH2C3D3N1V1 ZM9M2Z3B7P10名师精编优秀教案文档编码:CL9Y3C6P9F4 HH2C3D3N1V1 ZM9M2Z3B7P10文档编码:CL9Y3C6P9F4 HH2C3D3N1V1 ZM9M2Z3B7P10文档编码:CL9Y3C6P9F4 HH2C3D3N1V1 ZM9M2Z3B7P10文档编码:CL9Y3C6P9F4 HH2C3D3N1V1 ZM9M2Z3B7P10文档编码:CL9Y3C6P9F4 HH2C3D3N1V1 ZM9M2Z3B7P10文档编码:CL9Y3C6P9F4 HH2C3D3N1V1 ZM9M2Z3B7P10文档编码:CL9Y3C6P9F4 HH2C3D3N1V1 ZM9M2Z3B7P10文档编码:CL9Y3C6P9F4 HH2C3D3N1V1 ZM9M2Z3B7P10文档编码:CL9Y3C6P9F4 HH2C3D3N1V1 ZM9M2Z3B7P10文档编码:CL9Y3C6P9F4 HH2C3D3N1V1 ZM9M2Z3B7P10文档编码:CL9Y3C6P9F4 HH2C3D3N1V1 ZM9M2Z3B7P10文档编码:CL9Y3C6P9F4 HH2C3D3N1V1 ZM9M2Z3B7P10文档编码:CL9Y3C6P9F4 HH2C3D3N1V1 ZM9M2Z3B7P10文档编码:CL9Y3C6P9F4 HH2C3D3N1V1 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