正弦函数的图像

学习目标
1.会借助代数运算与几何直观,认识正弦函数的图像;[br]2.能运用“五点法”画出正弦函数在一个周期上的简图。
环节一 忆旧知·填要点
1 (1)利用单位圆定义任意角三角函数[br]任意角[math]\alpha[/math]的终边与单位圆交于[math]P\left(x,y\right)[/math],则[math]sin\alpha,cos\alpha[/math]所对应的值为
(2)如下图,任意角[math]\alpha[/math]的终边与单位圆交于[math]P\left(x,y\right)[/math],过[math]P[/math]向[math]x[/math]轴作垂线于[math]M[/math],则角[math]\alpha[/math]所对应的正弦线为[br][img]data:image/png;base64,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[/img]
2 作函数图像的常用三个步骤
3 (1)计算[math]sin0=[/math]
(2)计算[math]sin\frac{\pi}{2}=[/math]
(3)计算[math]sin\pi=[/math]
(4)计算[math]sin\frac{3\pi}{2}=[/math]
(5)计算[math]sin2\pi=[/math]
环节二 探新知·长知识
探究问题1:
探究问题1
(1)作出下列角[math]\alpha[/math]的正弦线[math]MP[/math];[br](请在导学案中作图,有疑问请在线提出)
(2)运用正弦线制作正弦函数y=sin x在[0,2π]上的图像;(请在线操作观察)
(3)正弦函数[math]y=sinx[/math]在[math]\left[0,2\text{π}\right][/math]上的图像有哪些关键点?
例1和练习1请在导学案中认真补充完成
在五点法作图中,请提出你的困难.[br](如没有,填写无)
拓展探究
函数[math]y=sinx[/math]的图像通过如下哪种变换可以得到[math]y=3+sinx[/math]的图像.
探究问题2
函数[math]y=sinx[/math]在[math]R[/math]上的函数图像.[br](课堂讲解中是否理解)
练习2
(1)函数y=sin x的最小正周期T是[u] .[/u]
(2)函数[math]y=f\left(x\right)[/math]的一个周期为[math]4[/math],[math]f\left(1\right)=-1[/math],则[math]f\left(5\right)[/math]=.
环节三 填重点·提能力
课堂小结
(1)五点法作[math]y=sinx[/math]在[math][0,2π][/math]的简图,五个关键点分别为
(2)函数[math]y=f\left(x\right)[/math],满足[math]f\left(x-1\right)=f\left(x\right)[/math],则[math]y=f\left(x\right)[/math]的一个周期为( )
(3)牢记三角函数在[0,2π]的简图.
Close

Information: 正弦函数的图像