由于三角函数y=Asin(ωx+φ)是由正弦函数y=sinu和一次函数u=ωx+φ复合而成的,而正弦函数y=sinu的对称轴是u=kπ+π/2(k∈Z),它的对称轴总是经过图像的最高点或者最低点。所以解决函数y=Asin(ωx+φ)的对称轴问题应从正弦函数的对称轴方程或函数关于直线对称的性质着手寻找解题思路。下面通过几道典型例题来谈一谈如何应用它们的对称轴来解题。例1如果函数y=sin 2x+acos 2x的图像关于直线x=-π/8对称,则a的值为()。 Since the trigonometric function y = Asin (ωx + φ) is composed of a sine function y = sinu and a linear function u = ωx + φ, the symmetry axis of the sine function y = sinu is u = kπ + π / 2 ∈Z) whose axis of symmetry always passes the highest or lowest point of the image. Therefore, to solve the problem of the symmetry axis of function y = Asin (ωx + φ), we should start with solving the problem from the symmetry axis function of sine function or the function about the symmetry of the line. Here are a few typical examples to talk about how to use their symmetry axis to solve the problem. Example 1 If the image of the function y = sin 2x + acos 2x is symmetric with respect to the line x = -π / 8, the value of a is ().