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以下为一些大学高数中三角函数图象相关的题目及答案示例： **一、图象变换类题目** 1. **题目** - 将函数\(y = \sin(\frac{\pi}{2}x+\frac{\pi}{4})\)的图象上各点的纵坐标不变，横坐标伸长到原来的2倍，再向右平移\(\frac{\pi}{4}\)个单位，求所得到的图象解析式。 2. **答案** - 首先，对于函数\(y = \sin(\frac{\pi}{2}x+\frac{\pi}{4})\)，横坐标伸长到原来的2倍（即\(x\)的系数变为原来的\(\frac{1}{2}\)），得到\(y=\sin(\frac{\pi}{4}x+\frac{\pi}{4})\)。 - 然后再向右平移\(\frac{\pi}{4}\)个单位，根据“左加右减”原则，\(x\)变为\(x-\frac{\pi}{4}\)，得到\(y = \sin[\frac{\pi}{4}(x - \frac{\pi}{4})+\frac{\pi}{4}]=\sin(\frac{\pi}{4}x-\frac{\pi^{2}}{16}+\frac{\pi}{4})=\sin(\frac{\pi}{4}x+\frac{(4 - \pi)\pi}{16})\)。 **二、根据图象求函数表达式类题目** 1. **题目** - 已知三角函数图象的最大值是\(\frac{3}{2}\)，从\(-\frac{\pi}{6}\)到\(\frac{5\pi}{6}\)是一个周期，图象为\(y = A\sin(\omega x+\varphi)\)（\(A>0,\omega>0\)且\(|\varphi|<\frac{\pi}{2}\)）的形式，求函数表达式。...

Two Zhao Pengs graduated from Sichuan University. Here is their resume: 1. Zhao Peng, male, born in June 1988, from Taizhou, Jiangsu Province. He is a lecturer at the School...

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