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第183章 诱导公式进阶篇(2 / 2)

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随后,戴浩文又写下了几组较为复杂的诱导公式,如:“sin(3π/2 + α) = -cosα,cos(3π/2 + α) = sinα ;sin(3π/2 - α) = -cosα,cos(3π/2 - α) = -sinα 。”

他缓声道:“这些公式看似繁杂,但只要我们理解了前面的基础,便能找到其中的规律。”

学子们纷纷点头,开始相互讨论。

戴浩文鼓励道:“大家不妨各抒己见,共同探讨。”

一时间,学堂里充满了学子们的讨论声。

一位学子说道:“先生,我觉得可以通过画图来理解这些公式。”

戴浩文回应道:“此法甚好,图形能让我们更直观地感受角度的变化与函数值的关系。”

又有学子提出疑问:“先生,这些公式在解决几何问题中如何应用?”

戴浩文思索片刻,回答道:“比如在计算不规则图形的边长或者角度时,通过诱导公式将三角函数值进行转换,便能找到解题的关键。”

接着,戴浩文在黑板上画出几个几何图形,结合诱导公式进行详细的讲解。

“看这道题,已知一个三角形的两个角分别为α和β,且α + β = 135°,求 sinα + sinβ 的值。我们可以利用诱导公式将其转换……”

学子们聚精会神地听着,不时点头。

讲解完例题后,戴浩文说道:“大家两两一组,相互出题练习,加深对这些公式的理解。”

学子们迅速行动起来,学堂里充满了思考和讨论的声音。

过了一会儿,戴浩文查看学子们的练习情况,不时给予指导和纠正。

“你这里的角度转换有误,再仔细想想。”

“这道题的思路很正确,继续保持。”

课程接近尾声,戴浩文总结道:“今日所学虽难,但只要大家勤加思考,多加练习,必能熟练掌握。下课!”

学子们起身行礼:“谢先生教诲!”

戴浩文看着学子们离去的背影,心中充满了欣慰,期待着他们能在数学的道路上越走越远……

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