“作业”作为学生学习真实信息的反馈载体，是教学活动的一个重要环节，是教师了解学生学习情况的一个重要手段，是课程资源的重要组成，是教师改进教学的重要依据，也是师生交流的一个平台。教师在教学过程中应充分发挥作业的诊断作用、强化作用、调节作用和教学作用。在三角函数学生作业中的错误主要有哪些类型？不同层次的学生作业中的错误有哪些差异？本研究针对这些问题对某重点中学的一个普通班和一个实验班的学生作业本进行了分析和研究，结合课堂观察和课后交流，得到以下结论：1．在所选样本的所有错误类型中，知识性错误为主，其次为逻辑性错误。(1)知识性错误主要错误表现为：a.混淆特殊角的各三角函数值，如混淆##和##、##和##、##和##、##和##等；b.对第3组诱导公式记忆 与 的三角函数间的关系、第4组诱导公式记忆 与 的三角函数间的关系记忆错误，尤其是第4组公式出现错误更多；c.解三角不等式时出错，主要的表现为忽视三角函数的周期性、混淆正弦函数与正切函数的周期、忽视正切函数的定义域。(2)逻辑性错误主要表现为：a.没有对结果进行分类或在分类讨论时分类不全；b.在三角不等式的解集与其它集合取交集时出现错误。2．在错误类型上两个班的差异如下：(1) 实验班错误类型多样，普通班错误类型较为单一；(2) 难题实验班主要为逻辑性错误，普通班主要为知识性错误；(3) 简单题实验班知识性错误、心理性错误并存，普通班主要是知识性错误。根据上述研究结果，本研究对三角函数的教学提出了三个方面的建议：(1) 进一步强化特殊角的三角函数值、诱导公式等基础知识，尤其重视强化普通班学生对这些基本概念和性质的理解和掌握；(2) 重视逻辑性错误的纠正，强调数学解题思维严谨性；(3) 讲同角三角函数的基本关系之前两个班级可以保持一致，之后普通班放慢速度，重视对知识缺陷的及时弥补。

Homework, as being able to provide feedback from the students, to expose their understandings of what have been taught, and to enrich the curriculum, forms an essential component of the teaching practice. According to the feedback, teachers diagnose students with misconceptions, improve the tuition, and enhance the communications with the students. Therefore, the diagnosing, reinforcing, regulating, and educating functions of the homework should be promoted. Especially, what are the common types of mistakes occur in the homework about the trigonometric functions? What are the differences among students of different levels? For answering the questions, we analyzed the submitted homework scripts of two classes, an ordinary class (OC) and an experimental class (EC), of students in a prestigious middle school. The data, combined with observations and communications on or after tutorials, provides us with the following conclusions:1, Among different kinds of mistakes in the samples, misconception forms the majority, with the corresponding mistakes happen more frequently than that of logic.(1) the misconception generally includes (a)getting the trigonometric function values of some specific angels mixed up, e.g. sinPi/6 with cosPi/6, sinPi/3 with cosPi/3,..., and sinPi/4 with tanPi/4; (b)failing in remembering the shift, symmetry or periodic formulas (esp. shift) correctly; (c)failing in solving the trigonometric inequalities, esp. on neglecting the periodicity, mixing the period of sine and tangent functions, or forgetting considering the domain of the tangent.(2) the logic mistakes includes in general (a)failing in doing necessary discussions correctly to different cases of some problems. (b)operating mistakes of finding intersections of some sets with the solutions of some trigonometric inequalities.2,The difference of two classes on typical mistakes:(1)types of mistakes vary widely in EC, while concentrate on some few ones in OC.(2)EC students make logic mistakes mainly, while OC students make misconceptions more frequently.(3)despite of misconceptions, EC students also make some psychological mistakes, while OC not that usual.Accordingly, the research suggests:1,Highlight the conception building, esp. for OC.2,Lay stress upon correcting the logistic mistakes, as well as helping students to develop strict and critical thinking.3,The two classes may be taught with a same pace on the basic knowledge, but then teachers for OC should slow down and conduct some necessary consolidations.