| Curriculum reform has been developed in an all-round way nationally. Hebei Province had put it into practice in Sept, 2009. The PEP version A, whose order was required 14253, was adopt as the teaching material. Trigonometric Functions, according to the outline of teaching material, was arranged in the second part of the first half of the semester (mid-terminal exam), instead of the latter half part formerly. In the senior middle school, Trigonometric Functions was the traditional content of the mathematics teaching material. In the reform, the new teaching material has changed tremendously ranging from content to method. It did not lay stress on the complicated identical transformation formula any more, but do delete some part of the former outline content. Meanwhile, it lowered the essential point on the induction formula and angle induced by the basic relation with the formula, emphasized on the image and nature of the Trigonometric Functions, and did put more emphasis on its model action and thought way in the combination between numbers and models. Under the interview between teachers and students, the writer, with the understanding and experience in math, found out that the students could not get the concept deeply, or hold the formula quickly. In this way, the ability of the combination between numbers and models should be improved. For example, many students can not distinguish acute angle of the trigonometric functions and arbitrary definition, can not use the trigonometric lines to analyze and solve problems.This article according to the new curriculum standard the request, as well as the student the question phenomenon which displays in the learning process, through measured that the examination paper and the interview and so on study the tool, from the following four aspects: the concept of Trigonometric Functions, the formula, the image and nature, and its application, Trigonometric function's concept, the formula, trigonometric function's image and the nature, the triangle function's application, divides the student according to the SOLO theory to the trigonometric function understanding level, through to Shijiazhuang different level four school high student (altogether 400) the answer paper carries on the quantification analysis and to the important concept nature analysis, the author discovered: (1) student"the function" the understanding is insufficient to the trigonometric function, did not know that the trigonometric function the independent variable and the function value respectively are anything, frequently makes a mistake. (2) students the function value and the independent variable to be very easy the trigonometric function sine and the cosine confuses . (3) not to be able to differentiate the acute angle trigonometric function and the random angle trigonometric function, some students as a result of the acute angle trigonometric function definition's negative migration, often treat as the obtuse angle function value the acute angle to ask. (4) students not to be able to use the directed line segment accurate expression function, if cannot correct make the directed line segment or use the correct symbolic representation. (5) the students use the unit circle and the function image insufficiency, cannot be full Direct-viewing analyzes using these geometries solves the question. (6) students cannot make the correct choice and carries on the formula to distort, what formula in the problem solving process should choose regarding any situation to distort not clearly. According to investigation and study's result, to enhance the teaching the validity and student's understanding level, about the random angle's trigonometric function, the unit circle application, the formula teaching, puts forward certain teaching proposal.
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