The reason why the conic curve of high school mathematics elective one is difficult to learn is often that the previous related content is not understood in place, and the headache and foot pain often cannot solve the problem, and it is necessary to start from the root. The root is actually in the trigonometric identity transformation, the plane vector, and the solution triangle, which on the surface seems simple, and the mastery is indeed better than other parts. Because of this, we tend to ignore the importance of this piece, this piece of content is actually a role in carrying on the upper and lower, the previous is a manifestation of the application of the nature of the function, the monotonicity of the function, parity, symmetry and periodicity can be perfectly reflected in the trigonometric function, and the function that was previously learned basically only involves one or two properties, and the four properties are used on a function, which belongs to the first time, and the nature of the learning function is prepared to a certain extent for learning the trigonometric function.
Looking back, spatial vectors are generalizations of planar vectors, solving triangles (solving right triangles and cosine theorems) is also widely used in stereo geometry, and the definition of trigonometric functions in right triangles and the quantitative product and angle of vectors are also used for the derivation of spatial distance formulas.
Later on to the conic curve part, the reason why it is difficult is first of all that it does not understand the nature of the slope of the straight line, and to see k as a slope, naturally can not find the idea. The essence of the slope of a straight line is the inclination angle, which is the tangent of the inclination angle, so with the slope (the slope of the straight line, the asymptote of the hyperbolic curve), we have to look at the angle, and the angle is the core of solving the geometric problem. This in turn uses the basic relationship of trigonometric functions of homogonometric angles and the definition of trigonometric functions in right triangles, and sine, cosine, and tangent know-one are the key and basic skills. The derivation of the formula including the string length also uses this original.
The second is that he is not familiar with solving the right triangle and the cosine theorem, and cannot even think of using the cosine theorem. Solving right triangles will only be solved using the Pythagorean theorem, not with the definition of the trigonometric function in a right triangle: a known sharp angle in a right triangle can find the other two sides and another sharp angle. The most common in geometry is actually triangles, so the key to analytic geometry is to solve triangles.
Again, the slope as an angle, you can use this angle to solve the triangle, in the right triangle and oblique triangle can come in handy, especially the cosine theorem is used to find the edge, very convenient, conical curve This piece of several problem types will use the cosine theorem.