在求解三角函数有关问题时,如果能利用三角函数的图象特征解题,将起到事半功倍的作用.下面举例说明.例1如果函数y=sin2x+acos2x的图象关于直线x=π8对称,那么a=.解析:利用正弦余弦函数的图象当自变量取对称轴时函数值取得最大或最小值这一特征得:|sin2.π8+acos2.π8|=a2+1=|22 When solving problems involving trigonometric functions, if you can use the image feature of the trigonometric function to solve the problem, it will play a multiplier role. Here is an example. Example 1 If the image of the function y=sin2x+acos2x is symmetrical about the line x=π8, Then a =. Analysis: image using sine cosine function When taking the axis of symmetry for the independent variable to obtain the maximum or minimum value of the feature: |sin2.π8+acos2.π8|=a2+1=|22