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高一下册《第6章 三角函数 一 三角函数的图像与性质 6.2 正切函数的图像与性质 探究与实践 课题三 制作弯管》优秀ppt课件
周期性
奇偶性
单调性
对称轴
对称中心
最大值
最小值
二、三角函数在其他领域中的应用
例3：阅读课本104页阅读材料《Mechanical Vibrations》
Mechanical vibration is a very important and commonplace physical phenomenon. The pleasant sounds produced by many musical instruments result from the vibrations of tightly stretched strings or wooden reeds. Vibrations can also be destructive. The collapse of the Tacoma Narrows Bridge in 1940 and the failure of aircraft components due to metal fatigue are examples of disastrous side effects of mechanical vibrations.
三角函数与音乐
声音的本质是波。如图1,是小提琴的声音的图形，这种声音听起来是悦耳的，称为乐音。
法国数学家傅里叶说：“一个周期函数可以表示成正弦函数的和。”
这是由三个具有适当音量，频率分别是500Hz,
1000Hz,1500Hz的音叉同时发声而产生，因此从理论上讲，完全可以由音叉来演奏贝多芬的第九交响曲
Although mechanical vibrations can be very complicated, there is a simple physical model that mathematicians, engineers, and scientists use to study their most basic features. It consists of a weight w hanging from the lower end of a spring whose upper end is attached to a support. If the weight is hanging motionless from the spring, the downward pull of gravity on the weight is exactly counterbalanced by the upward pull on the weight by the stretched spring, and we say that the weight-spring system is in equilibrium position. If the weight is disturbed from its equilibrium position by, for example, giving it a shove upward or pulling it downward and releasing it then it will bounce up and down around its equilibrium position.
由牛顿第二定律
得
再由运动学公式
得
三、制作弯管
阅读课本96页课题三《制作弯管》
探究一：
用A4纸制作一个圆柱，斜截圆柱一分为二，要确保界面是平面。可以将斜截面置于桌面来检验，若截口与桌面没有空隙则为平面。
把其中一个斜截圆柱的侧面剪开并摊平，如图所示。